Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-24T01:46:07.613Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  20 April 2018

Miguel Cabrera García
Affiliation:
Universidad de Granada
Ángel Rodríguez Palacios
Affiliation:
Universidad de Granada
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Primary Sources

Acosta, M. D., Becerra, J., and Rodríguez, A., Weakly open sets in the unit ball of the projective tensor product of Banach spaces. J. Math. Anal. Appl. 383 (2011), 461–73.Google Scholar
Adams, J. F., On the structure and applications of the Steenrod algebra. Comment. Math. Helv. 32 (1958), 180214.CrossRefGoogle Scholar
Akemann, C. A. and Pedersen, G. K., Complications of semicontinuity in C -algebra theory. Duke Math. J. 40 (1973), 785–95. 346Google Scholar
Akemann, C. A. and Pedersen, G. K., Facial structure in operator algebra theory. Proc. London Math. Soc. 64 (1992), 418–48.Google Scholar
Akemann, C. A. and Weaver, N., Geometric characterizations of some classes of operators in C -algebras and von Neumann algebras. Proc. Amer. Math. Soc. 130 (2002), 3033–7.Google Scholar
Albert, A. A., On a certain algebra of quantum mechanics. Ann. of Math. 35 (1934), 6573. Reprinted in [692], pp. 85–93.CrossRefGoogle Scholar
Albert, A. A., Quadratic forms permitting composition. Ann. of Math. 43 (1942), 161–77. Reprinted in [692], pp. 219–35.Google Scholar
Albert, A. A., The radical of a non-associative algebra. Bull. Amer. Math. Soc. 48 (1942), 891–7. Reprinted in [692], pp. 277–83. 546Google Scholar
Albert, A. A., Absolute valued real algebras. Ann. of Math. 48 (1947), 495501. Reprinted in [691], pp. 643–9.Google Scholar
Albert, A. A., A structure theory for Jordan algebras. Ann. of Math. 48 (1947), 546–67. Reprinted in [692], pp. 401–22.Google Scholar
Albert, A. A., On the power-associativity of rings. Summa Brasil. Math. 2 (1948), 2132. Reprinted in [692], pp. 423–35.Google Scholar
Albert, A. A., Power-associative rings. Trans. Amer. Math. Soc. 608 (1948), 552–93. Reprinted in [692], pp. 437–78. 273Google Scholar
Albert, A. A., Absolute valued algebraic algebras. Bull. Amer. Math. Soc. 55 (1949), 763–8. Reprinted in [691], pp. 651–6.Google Scholar
Albert, A. A., A note of correction. Bull. Amer. Math. Soc. 55 (1949), 1191.Google Scholar
Alfsen, E. M., Shultz, F. W., and Størmer, E., Gelfand, ANeumark theorem for Jordan algebras. Adv. Math. 28 (1978), 1156. 398, 401Google Scholar
Allan, G. R., Some simple proofs in holomorphic spectral theory. In Perspectives in operator theory, pp. 915, Banach Center Publ. 75, Polish Acad. Sci. Inst. Math., Warsaw, 2007.Google Scholar
Alvermann, K., The multiplicative triangle inequality in noncommutative JB- and JB -algebras. Abh. Math. Sem. Univ. Hamburg 55 (1985), 91–6.Google Scholar
Alvermann, K., Real normed Jordan Banach algebras with an involution. Arch. Math. (Basel) 47 (1986), 135–50.CrossRefGoogle Scholar
Alvermann, K. and Janssen, G., Real and complex non-commutative Jordan Banach algebras. Math. Z. 185 (1984), 105–13. xix, xx, 19, 267, 268, 334, 335, 398, 411, 421Google Scholar
Ambrose, W., Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364886. xxiii, xxv, 477, 545, 550Google Scholar
Anquela, J. A., Montaner, F., and Cortés, T., On primitive Jordan algebras. J. Algebra 163 (1994), 663–74. xxii, 462, 466CrossRefGoogle Scholar
Aparicio, C., Ocaña, F. G., Payá, R., and Rodríguez, A., A non-smooth extension of Fréchet differentiability of the norm with applications to numerical ranges. Glasgow Math. J. 28 (1986), 121–37.Google Scholar
Aparicio, C. and Rodríguez, A., Sobre el espectro de derivaciones y automorfismos de las álgebras de Banach. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 79 (1985), 113–18.Google Scholar
Araki, H. and Elliott, G. A., On the definition of C -algebras. Publ. Res. Inst. Math. Sci. 9 (1973/74), 93112.Google Scholar
Arazy, J., Isometries of Banach algebras satisfying the von Neumann inequality. Math. Scand. 74 (1994), 137–51. 136, 207Google Scholar
Arazy, J. and Solel, B., Isometries of nonselfadjoint operator algebras. J. Funct. Anal. 90 (1990), 284305. 207CrossRefGoogle Scholar
Arendt, W., Chernoff, P. R., and Kato, T., A generalization of dissipativity and positive semigroups. J. Operator Theory 8 (1982), 167–80.Google Scholar
Arens, R., Operations induced in function classes. Monatsh. Math. 55 (1951), 119.CrossRefGoogle Scholar
Arens, R., The adjoint of a bilinear operation. Proc. Amer. Math. Soc. 2 (1951), 839–48.Google Scholar
Arens, R. and Kaplansky, I., Topological representation of algebras. Trans. Amer. Math. Soc. 63 (1948), 457–81.Google Scholar
Argyros, S. A. and Felouzis, V., Interpolating hereditarily indecomposable Banach spaces. J. Amer. Math. Soc. 13 (2000), 243–94.CrossRefGoogle Scholar
Argyros, S. A. and Haydon, R. G., A hereditarily indecomposable L -space that solves the scalar-plus-compact problem. Acta Math. 206 (2011), 154.Google Scholar
Argyros, S. A., López-Abad, J., and Todorcevic, S., A class of Banach spaces with few non-strictly singular operators. J. Funct. Anal. 222 (2005), 306–84.Google Scholar
Aron, R. M. and Lohman, R. H., A geometric function determined by extreme points of the unit ball of a normed space. Pacific J. Math. 127 (1987), 209–31.Google Scholar
Arosio, A., Locally convex inductive limits of normed algebras. Rend. Sem. Mat. Univ. Padova 51 (1974), 333–59.Google Scholar
Auerbach, H., Sur les groupes linéaires I, II, III. Studia Math . 4 (1934), 113–27; Ibid. 4 (1934), 158–66; Ibid. 5 (1935), 43–9.Google Scholar
Aupetit, B., Symmetric almost commutative Banach algebras. Notices Amer. Math. Soc. 18 (1971), 559–60.Google Scholar
Aupetit, B., Caractérisation spectrale des algèbres de Banach commutatives. Pacific J. Math. 63 (1976), 2335.CrossRefGoogle Scholar
Aupetit, B., Caractérisation spectrale des algèbres de Banach de dimension finie. J. Funct. Anal. 26 (1977), 232–50.Google Scholar
Aupetit, B., The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras. J. Funct. Anal. 47 (1982), 16. x, 597Google Scholar
Aupetit, B., Recent trends in the field of Jordan–Banach algebras. In [1189], pp. 9–19. 597Google Scholar
Aupetit, B., Analytic Multifunctions and their applications. In Complex potential theory (ed. Gauthier, P. M.), pp. 174, Kluwer Academic Publishers, Dordrecht– Boston–London 1994.Google Scholar
Aupetit, B., Spectral characterization of the socle in Jordan–Banach algebras. Math. Proc. Cambridge Philos. Soc. 117 (1995), 479–89. 601CrossRefGoogle Scholar
Aupetit, B., Trace and spectrum preserving linear mappings in Jordan–Banach algebras. Monatsh. Math. 125 (1998), 179–87. 601Google Scholar
Aupetit, B. and Baribeau, L., Sur le socle dans les algèbres de Jordan–Banach. Canad. J. Math. 41 (1989), 1090–100. 599Google Scholar
Aupetit, B. and Maouche, A., Trace and determinant in Jordan–Banach algebras. Publ. Mat. 46 (2002), 316. 601Google Scholar
Aupetit, B. and Mathieu, M., The continuity of Lie homomorphisms. Studia Math. 138 (2000), 193–99. 603Google Scholar
Aupetit, B. and Youngson, M. A., On symmetry of Banach Jordan algebras. Proc. Amer. Math. Soc. 91 (1984), 364–6. 597Google Scholar
Avilés, A. and Koszmider, P., A Banach space in which every injective operator is surjective. Bull. London Math. Soc. 45 (2013), 1065–74.Google Scholar
Baer, R., Radical ideals. Amer. J. Math. 65 (1943), 537–68.Google Scholar
Baez, J. C., The octonions. Bull. Amer. Math. Soc. 39 (2002), 145205. Errata. Ibid. 42 (2005), 213.Google Scholar
Baillet, M., Analyse spectrale des opérateurs hermitiens d’une espace de Banach. J. London Math. Soc. 19 (1979), 497508.Google Scholar
Balachandran, V. K., Simple L -algebras of classical type. Math. Ann. 180 (1969), 205–19. 554Google Scholar
Balachandran, V. K. and Rema, P. S., Uniqueness of the norm topology in certain Banach Jordan algebras. Publ. Ramanujan Inst. 1 (1969), 283–9. 597Google Scholar
Balachandran, V. K. and Swaminatan, N., Real H -algebras. J. Funct. Anal. 65 (1986), 6475. 551CrossRefGoogle Scholar
Bandyopadhyay, P., Jarosz, K., and Rao, T. S. S. R. K., Unitaries in Banach spaces. Illinois J. Math. 48 (2004), 339–51.Google Scholar
Barnes, B. A., Locally B -equivalent algebras. Trans. Amer. Math. Soc. 167 (1972), 435–42.Google Scholar
Barnes, B. A., Locally B -equivalent algebras II. Trans. Amer. Math. Soc. 176 (1973), 297303.Google Scholar
Barnes, B. A., A note on invariance of spectrum for symmetric Banach ∗-algebras. Proc. Amer. Math. Soc. 126 (1998), 3545–7.Google Scholar
Barton, T. J. and Friedman, Y., Bounded derivations of JB -triples. Quart. J. Math. Oxford 41 (1990), 255–68. xx, 274, 337, 338Google Scholar
Bauer, F. L., On the field of values subordinate to a norm. Numer. Math. 4 (1962), 103–11.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Banach algebras with large groups of unitary elements. Quart. J. Math. Oxford 58 (2007), 203–20.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Banach spaces whose algebras of operators have a large group of unitary elements. Math. Proc. Camb. Phil. Soc. 144 (2008), 97108.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Nonassociative unitary Banach algebras. J. Algebra 320 (2008), 3383–97.Google Scholar
Becerra, J., Cowell, S., Rodríguez, A., and Wood, G. V., Unitary Banach algebras. Studia Math. 162 (2004), 2551.Google Scholar
Becerra, J., López, G., Peralta, A. M., and Rodríguez, A., Relatively weakly open sets in closed balls of Banach spaces, and real JB -triples of finite rank. Math. Ann. 330 (2004), 4558. 243, 274, 336Google Scholar
Becerra, J., López, G., and Rodríguez, A., Relatively weakly open sets in closed balls of C -algebras. J. London Math. Soc. 68 (2003), 753–61. 274, 336, 421Google Scholar
Becerra, J., Moreno, A., and Rodríguez, A., Absolute-valuable Banach spaces. Illinois J. Math. 49 (2005), 121–38.Google Scholar
Becerra, J. and Peralta, A. M., Subdifferentiability of the norm and the Banach–Stone theorem for real and complex JB -triples. Manuscripta Math. 114 (2004), 503–16.Google Scholar
Becerra, J. and Rodríguez, A., Isometric reflections on Banach spaces after a paper of A. Skorik and M. Zaidenberg. Rocky Mountain J. Math. 30 (2000), 6383.Google Scholar
Becerra, J. and Rodríguez, A., Transitivity of the norm on Banach spaces having a Jordan structure, Manuscripta Math. 102 (2000), 111–27. 210Google Scholar
Becerra, J. and Rodríguez, A., Characterizations of almost transitive superrreflexive Banach spaces. Comment. Math. Univ. Carolinae 42 (2001), 629–36.Google Scholar
Becerra, J. and Rodríguez, A., Transitivity of the norm on Banach spaces. Extracta Math. 17 (2002), 158.Google Scholar
Becerra, J. and Rodríguez, A., Strong subdifferentiability of the norm on JB -triples. Quart. J. Math. Oxford 54 (2003), 381–90.Google Scholar
Becerra, J. and Rodríguez, A., Big points in C -algebras and JB -triples. Quart. J. Math. Oxford 56 (2005), 141–64.Google Scholar
Becerra, J. and Rodríguez, A., Absolute-valued algebras with involution, and infinite-dimensional Terekhin’s trigonometric algebras. J. Algebra 293 (2005), 448–56.Google Scholar
Becerra, J. and Rodríguez, A., Non self-adjoint idempotents in C - and JB -algebras. Manuscripta Math. 124 (2007), 183–93.Google Scholar
Becerra, J. and Rodríguez, A., C - and JB -algebras generated by a non-self-adjoint idempotent. J. Funct. Anal. 248 (2007), 107–27.Google Scholar
Becerra, J. and Rodríguez, A., Locally uniformly rotund points in convex-transitive Banach spaces. J. Math. Anal. Appl. 360 (2009), 108–18.Google Scholar
Becerra, J., Rodríguez, A., and Wood, G. V., Banach spaces whose algebras of operators are unitary: a holomorphic approach. Bull. London Math. Soc. 35 (2003), 218–24. 210Google Scholar
Beddaa, A. and Oudadess, M., On a question of A. Wilansky in normed algebras. Studia Math. 95 (1989), 175–7.Google Scholar
Behncke, H., Hermitian Jordan Banach algebras. J. London Math. Soc. 20 (1979), 327–33. 597Google Scholar
Behncke, H. and Nyamwala, F. O., Two projections and one idempotent. Int. J. Pure Appl. Math. 52 (2009), 501–10.Google Scholar
Bell, J. P. and Small, L. W., A question of Kaplansky. J. Algebra 258 (2002), 386–8.Google Scholar
Bensebah, A., JV-algèbres et JH -algèbres. Canad. Math. Bull. 34 (1991), 447–55. 549, 597Google Scholar
Bensebah, A., Weakness of the topology of a JB -algebra. Canad. Math. Bull. 35 (1992), 449–54. 597Google Scholar
Benslimane, M. and Boudi, N., Alternative Noetherian Banach Algebras. Extracta Math. 12 (1997), 41–6. 601Google Scholar
Benslimane, M. and Boudi, N., Noetherian Jordan Banach algebras are finite-dimensional. J. Algebra 213 (1999), 340–50. 601Google Scholar
Benslimane, M., Fernández, A., and Kaidi, A., Caractérisation des algèbres de Jordan– Banach de capacité finie. Bull. Sci. Math. 112 (1988), 473–80. 597, 598, 599Google Scholar
Benslimane, M., Jaa, O., and Kaidi, A., The socle and the largest spectrum finite ideal. Quart. J. Math. Oxford 42 (1991), 17. 599, 601Google Scholar
Benslimane, M. and Kaidi, A., Structure des algèbres de Jordan–Banach non commutatives complexes régulières ou semi-simples à spectre fini. J. Algebra 113 (1988), 201–6. xxv, 596, 597, 598CrossRefGoogle Scholar
Benslimane, M. and Merrachi, N., Algèbres de Jordan Banach vérifiant ‖x‖‖x −1‖ = 1. J. Algebra 206 (1998), 129–34.Google Scholar
Benslimane, M. and Merrachi, N., Algèbres à puissances associatives normées sans J-diviseurs de zéro. Algebras Groups Geom. 16 (1999), 355–61.Google Scholar
Benslimane, M. and Moutassim, A., Some new class of absolute-valued algebras with left-unit. Adv. Appl. Clifford Algebras 21 (2011), 3140.Google Scholar
Benslimane, M. and Rodríguez, A., Caractérisation spectrale des algèbres de Jordan Banach non commutatives complexes modulaires annihilatrices. J. Algebra 140 (1991), 344–54. 599Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie derivations on Banach algebras. Proc. Edinburgh Math. Soc. 41 (1998), 625–30.Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie mappings of the skew elements of Banach algebras with involution. Proc. Amer. Math. Soc. 126 (1998), 2717–20.Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie isomorphisms of Banach algebras. Bull. London Math. Soc. 31 (1999), 610.Google Scholar
Berenguer, M. I. and Villena, A. R., On the range of a Lie derivation on a Banach algebra. Comm. Algebra 28 (2000), 1045–50.Google Scholar
Berkson, E., Some characterizations of C -algebras. Illinois J. Math. 10 (1966), 18.Google Scholar
Beurling, A., Sur les intégrales de Fourier absolument convergentes et leur application à fonctionelle. In Neuvième congrès des mathématiciens scandinaves. Helsingfors, 1938, pp. 345–66.Google Scholar
Biss, D. K., Christensen, J. D., Dugger, D., and Isaksen, D. C., Large annihilators in Cayley–Dickson algebras II. Bol. Soc. Mat. Mexicana 13 (2007), 269–92.Google Scholar
Biss, D. K., Christensen, J. D., Dugger, D., and Isaksen, D. C., Eigentheory of Cayley– Dickson algebras. Forum Math. 21 (2009), 833–51.Google Scholar
Biss, D. K., Dugger, D., and Isaksen, D. C., Large annihilators in Cayley–Dickson algebras. Comm. Algebra 36 (2008), 632–64.Google Scholar
Blecher, D. and Magajna, B., Dual operator systems. Bull. London Math. Soc. 43 (2011), 311–20.Google Scholar
Blecher, D. P., Ruan, Z.-J., and Sinclair, A. M., A characterization of operator algebras. J. Funct. Anal. 89 (1990), 188201.Google Scholar
Boas, R. P., Entire functions of exponential type. Bull. Amer. Math. Soc. 48 (1942), 839–49.Google Scholar
Bohnenblust, H. F. and Karlin, S., Geometrical properties of the unit sphere of a Banach algebra. Ann. of Math. 62 (1955), 217–29.Google Scholar
Bollobás, B., An extension to the theorem of Bishop and Phelps. Bull. London Math. Soc. 2 (1970), 181–2.Google Scholar
Bollobás, B., The numerical range in Banach algebras and complex functions of exponential type. Bull. London Math. Soc. 3 (1971), 2733.Google Scholar
Bonsall, F. F., A minimal property of the norm in some Banach algebras. J. London Math. Soc. 29 (1954), 156–64.Google Scholar
Bonsall, F. F., Locally multiplicative wedges in Banach algebras. Proc. London Math. Soc. 30 (1975), 239–56.Google Scholar
Bonsall, F. F., Jordan algebras spanned by Hermitian elements of a Banach algebra. Math. Proc. Cambridge Philos. Soc. 81 (1977), no. 1, 313.Google Scholar
Bonsall, F. F., Jordan subalgebras of Banach algebras. Proc. Edinburgh Math. Soc. 21 (1978), 103–10.Google Scholar
Bonsall, F. F. and Crabb, M. J., The spectral radius of a Hermitian element of a Banach algebra. Bull. London Math. Soc. 2 (1970), 178–80.Google Scholar
Bonsall, F. F. and Duncan, J., Dually irreducible representations of Banach algebras, Quart. J. Math. Oxford 19 (1968), 97111.Google Scholar
Bott, R. and Milnor, J., On the parallelizability of the spheres. Bull. Amer. Math. Soc. 64 (1958), 87–9.Google Scholar
Böttcher, A. and Spitkovsky, I. M., A gentle guide to the basics of two projections theory. Linear Algebra Appl. 432 (2010), 1412–59.CrossRefGoogle Scholar
Boudi, N., On Jordan Banach algebras with countably generated inner ideals. Algebra Colloq. 17 (2010), 211–22. 601Google Scholar
Boudi, N., Marhnine, H., Zarhouti, C., Fernández, A., and García, E., Noetherian Banach Jordan pairs. Math. Proc. Cambridge Philos. Soc. 130 (2001), 2536. 601Google Scholar
Bouhya, K. and Fernández, A., Jordan-∗-triples with minimal inner ideals and compact JB -triples. Proc. London Math. Soc. 68 (1994), 380–98. 241, 461, 603Google Scholar
Boyko, K., Kadets, V., Martín, M., and Werner, D., Numerical index of Banach spaces and duality. Math. Proc. Cambridge Philos. Soc. 142 (2007), 93102.Google Scholar
Bratteli, O. and Robinson, D. W., Unbounded derivations of C -algebras. II. Comm. Math. Phys. 46 (1976), 1130.Google Scholar
Braun, R. B., Structure and representations of non-commutative C -Jordan algebras. Manuscripta Math. 41 (1983), 139–71. xx, xxi, 398, 411, 421Google Scholar
Braun, R. B., A Gelfand–Neumark theorem for C -alternative algebras. Math. Z. 185 (1984), 225–42. xx, xxi, 411Google Scholar
Braun, R. B., Kaup, W., and Upmeier, H., A holomorphic characterization of Jordan C -algebras. Math. Z. 161 (1978), 277–90. 210Google Scholar
Brelot, M., Points irréguliers et transformations continues en théorie du potentiel. J. Math. Pures Appl. 19 (1940), 319–37.Google Scholar
Brelot, M., Sur les ensembles effilés. Bull. Sci. Math. 68 (1944), 1236.Google Scholar
Bremner, M. and Hentzel, I., Identities for algebras obtained from the Cayley–Dickson process. Comm. Algebra 29 (2001), 3523–34.Google Scholar
Brešar, M., Cabrera, M., Fosner, M., and Villena, A. R., Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan–Banach algebras. Studia Math. 169 (2005), 207–28. 602Google Scholar
Brešar, M., Šemrl, P., and Špenko, S., On locally complex algebras and low-dimensional Cayley–Dickson algebras. J. Algebra 327 (2011), 107–25.Google Scholar
Browder, A., States, numerical ranges, etc.. In Proceedings of the Brown informal analysis seminar. Summer, 1969 (revised version, Summer of 2012).Google Scholar
Browder, A., On Bernstein’s inequality and the norm of Hermitian operators. Amer. Math. Monthly 78 (1971), 871–3.Google Scholar
Brown, R., On generalized Cayley–Dickson algebras. Pacific J. Math. 20 (1967), 415–22.Google Scholar
Bunce, L. J., Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., A Saitô–Tomita– Lusin theorem for JB -triples and applications. Quart. J. Math. Oxford 57 (2006), 3748.Google Scholar
Bunce, L. J. and Peralta, A. M., Images of contractive projections on operator algebras. J. Math. Anal. Appl. 272 (2002), 5566. 210CrossRefGoogle Scholar
Burgos, M. J., Peralta, A. M., Ramírez, M. I., and Ruiz, E. E., Von Neumann regularity in Jordan–Banach triples. In [704], pp. 67–88.Google Scholar
Busby, R. C., Double centralizers and extensions of C -algebras. Trans. Amer. Math. Soc. 132 (1968), 7999.Google Scholar
Cabello, F., Regards sur le problème des rotations de Mazur. Extracta Math. 12 (1997), 97116.Google Scholar
Cabrera, M., El Marrakchi, A., Martínez, J., and Rodríguez, A., An Allison– Kantor–Koecher–Tits construction for Lie H -algebras. J. Algebra 164 (1994), 361408. xxv, 556Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Malcev H -algebras. Math. Proc. Cambridge Phil. Soc. 103 (1988), 463–71. xxv, 553, 554Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Nonassociative real H -algebras. Publ. Mat. 32 (1988), 267–74. xxiv, 549, 551Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., A note on real H -algebras. Math. Proc. Cambridge Phil. Soc. 105 (1989), 131–2.CrossRefGoogle Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Structurable H -algebras. J. Algebra 147 (1992), 1962. xxv, 552, 553, 555, 556Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., Normed versions of the Zel’manov prime theorem: positive results and limits. In: Operator theory, operator algebras and related topics (Timisoara, 1996) (eds. Gheondea, A., Gologan, R. N. and Timotin, D.), Theta Found., Bucharest, 1997, pp. 6577. 462, 463, 465Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., Zel’manov’s theorem for primitive Jordan–Banach algebras. J. London Math. Soc. 57 (1998), 231–44. xxii, 463, 464, 465Google Scholar
Cabrera, M., Moreno, A., Rodríguez, A., and Zel’manov, E. I., Jordan polynomials can be analytically recognized. Studia Math. 117 (1996), 137–47. xxii, 437, 470Google Scholar
Cabrera, M. and Rodríguez, A., Extended centroid and central closure of semiprime normed algebras: a first approach. Comm. Algebra 18 (1990), 2293–326. xxiii, 408, 546, 555Google Scholar
Cabrera, M. and Rodríguez, A., Nonassociative ultraprime normed algebras. Quart. J. Math. Oxford 43 (1992), 17. xxi, xxiii, 409, 546Google Scholar
Cabrera, M. and Rodríguez, A., New associative and nonassociative Gelfand–Naimark theorems. Manuscripta Math. 79 (1993), 197208.Google Scholar
Cabrera, M. and Rodríguez, A., Zel’manov theorem for normed simple Jordan algebras with a unit. Bull. London Math. Soc. 25 (1993), 5963. xxii, 467, 468Google Scholar
Cabrera, M. and Rodríguez, A., Non-degenerately ultraprime Jordan–Banach algebras: a Zel’manovian treatment. Proc. London Math. Soc. 69 (1994), 576604. xxii, 409, 468, 469Google Scholar
Cabrera, M. and Rodríguez, A., A new simple proof of the Gelfand–Mazur–Kaplansky theorem. Proc. Amer. Math. Soc. 123 (1995), 2663–6. 408Google Scholar
Cabrera, M. and Rodríguez, A., On the Gelfand–Naimark axiom ‖a a‖ = ‖a ‖‖a. Quart. J. Math. Oxford 63 (2012), 855–60.Google Scholar
Calderón, A., Kaidi, A., Martín, C., Morales, A., Ramírez, M., and Rochdi, A., Finite-dimensional absolute-valued algebras. Israel J. Math. 184 (2011), 193220.Google Scholar
Calderón, A. J. and Martín, C., Two-graded absolute valued algebras. J. Algebra 292 (2005), 492515.Google Scholar
Calkin, J. W., Two-sided ideals and congruences in the ring of bounded operators in Hilbert space. Ann. of Math. 42 (1941), 839–73.Google Scholar
Caradus, S. R., Operators of Riesz type. Pacific J. Math. 18 (1966), 6171.Google Scholar
Cartan, E., Les groupes bilinéaires et les systèmes de nombres complexes. Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 12 (1898), 199. Reprinted in Oeuvres Complètes, Vol II, Paris, Gauthier-Villars, 1952.Google Scholar
Cartan, H., Théorie générale du balayage en potentiel newtonien. Ann. Univ. Grenoble. Sect. Sci. Math. Phys. 22 (1946), 221–80.Google Scholar
Casazza, P. G., Approximation properties. In Handbook of the geometry of Banach spaces, Vol. I (eds. Johnson, W. B. and Lindenstrauss, J.), pp. 271316, North-Holland, Amsterdam, 2001. Addenda and corrigenda: In [757], pp. 1817–18.Google Scholar
Castellón, A. and Cuenca, J. A., Isomorphisms of H -triple systems. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 19 (1992), 507–14. 561Google Scholar
Castellón, A. and Cuenca, J. A., Associative H -triple systems. In [734], pp. 45–67. 551, 561Google Scholar
Cayley, A., On Jacobi’s elliptic functions, in reply to the Rev. B. Bronwin; and on quaternions. Philos. Mag. 26 (1845), 208–11.Google Scholar
Cedilnik, A. and Rodríguez, A., Continuity of homomorphisms into complete normed algebraic algebras. J. Algebra 264 (2003), 614. 595, 596Google Scholar
Cedilnik, A. and Zalar, B., Nonassociative algebras with submultiplicative bilinear form. Acta Math. Univ. Comenian. 63 (1994), 285301.Google Scholar
Chan, K.-C. and Dokovic, D. Z., Conjugacy classes of subalgebras of the real sedenions. Canad. Math. Bull. 49 (2006), 492507.Google Scholar
Chandid, A. and Rochdi, A., Mutations of absolute valued algebras. Int. J. Algebra 2 (2008), 357–68.Google Scholar
Choi, M. D. and Effros, E., Injectivity and operator spaces. J. Funct. Anal. 24 (1974), 156209.Google Scholar
Chonghu, W., Some geometric properties of Banach spaces and x+λy‖−‖x λ on it. J. Nanjing Univ. 6 (1989), 3745.Google Scholar
Chu, C.-H., Dang, T., Russo, B., and Ventura, B., Surjective isometries of real C -algebras. J. London Math. Soc. 47 (1993), 97118.Google Scholar
Chu, C.-H., Iochum, B., and Loupias, G., Grothendieck’s theorem and factorization of operators in Jordan triples. Math. Ann. 284 (1989), 4153. xix, 2, 245, 267, 343, 344, 346Google Scholar
Chu, C.-H. and Mellon, P., Jordan structures in Banach spaces and symmetric manifolds. Expos. Math. 16 (1998), 157–80. 211Google Scholar
Chu, C.-H. and Velasco, M. V., Automatic continuity of homomorphisms in nonassociative Banach algebras. Canadian J. Math. 65 (2013), 9891004.Google Scholar
Civin, P. and Yood, B., Lie and Jordan structures in Banach algebras. Pacific J. Math. 15 (1965), 775–97. 583Google Scholar
Cleveland, S. B., Homomorphisms of non-commutative ∗-algebras. Pacific J. Math. 13 (1963), 1097–109.Google Scholar
Cobalea, M. A. and Fernández, A., Prime noncommutative Jordan algebras and central closure. Algebras Groups Geom. 5 (1988), 129–36. 408Google Scholar
Cohn, P. M., On homomorphic images of special Jordan algebras. Canadian J. Math. 6 (1954), 253–64.Google Scholar
Contreras, M. D. and Payá, R., On upper semicontinuity of duality mappings. Proc. Amer. Math. Soc. 121 (1994), 451–9.Google Scholar
Contreras, M. D., Payá, R., and Werner, W., C -algebras that are I-rings. J. Math. Anal. Appl. 198 (1996), 227–36.Google Scholar
Cowie, E. R., An analytic characterization of groups with no finite conjugacy classes. Proc. Amer. Math. Soc. 87 (1983), 710.Google Scholar
Crabb, M. J., Duncan, J., and McGregor, C. M., Some extremal problems in the theory of numerical ranges. Acta Math. 128 (1972), 123–42.Google Scholar
Crabb, M. J., Duncan, J., and McGregor, C. M., Characterizations of commutativity for C -algebras. Glasgow Math. J. 15 (1974), 172–5. 400Google Scholar
Crabb, M. J. and McGregor, C. M., Numerical ranges of powers of Hermitian elements. Glasgow Math. J. 28 (1986), 3745.Google Scholar
Crabb, M. J. and McGregor, C. M., Polynomials in a Hermitian element. Glasgow Math. J. 30 (1988), 171–6.Google Scholar
Cuartero, B. and Galé, J. E., Locally PI-algebras over valued fields. In Aportaciones Matemáticas en Memoria del Profesor V. M. Onieva, pp. 137–45, Santander, Universidad de Cantabria, 1991.Google Scholar
Cuartero, B. and Galé, J. E., Bounded degree of algebraic topological algebras. Comm. Algebra 422 (1994), 329–37.Google Scholar
Cuartero, B., Galé, J. E., Rodríguez, A., and Slinko, A. M., Bounded degree of weakly algebraic topological Lie algebras. Manuscripta Math. 81 (1993), 129–39. 658Google Scholar
Cudia, D. F., The geometry of Banach spaces. Smoothness. Trans. Amer. Math. Soc. 110 (1964), 284314.Google Scholar
Cuenca, J. A., On one-sided division infinite-dimensional normed real algebras. Publ. Mat. 36 (1992), 485–8.Google Scholar
Cuenca, J. A., On composition and absolute-valued algebras. Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), 717–31.Google Scholar
Cuenca, J. A., On an Ingelstam’s theorem. Comm. Algebra 35 (2007), 4057–67.Google Scholar
Cuenca, J. A., On structure theory of pre-Hilbert algebras. Proc. R. Soc. Edinburgh 139A (2009), 303–19.Google Scholar
Cuenca, J. A., Some classes of pre-Hilbert algebras with norm-one central idempotent. Israel J. Math. 193 (2013), 343–58.Google Scholar
Cuenca, J. A., A new class of division algebras and Wedderburn’s and Frobenius’ Theorems. Preprint 2012.Google Scholar
Cuenca, J. A., Third-power associative absolute vaued algebras with a nonzero idempotent commuting with all idempotents. Publ. Mat. 58 (2014), 469–84.Google Scholar
Cuenca, J. A., García, A., and Martín, C.. Structure theory for L -algebras, Math. Proc. Cambridge Phil. Soc. 107 (1990), 361–5. xxv, 554Google Scholar
Cuenca, J. A. and Rodríguez, A., Isomorphisms of H -algebras. Math. Proc. Cambridge Phil. Soc. 97 (1985), 93–9. xxiv, 546, 549Google Scholar
Cuenca, J. A. and Rodríguez, A., Structure theory for noncommutative Jordan H -algebras. J. Algebra 106 (1987), 114. xxiii, xxv, 545, 552, 553Google Scholar
Cuenca, J. A. and Rodríguez, A., Absolute values on H -algebras. Comm. Algebra 23 (1995), 1709–40. 481Google Scholar
Cuntz, J., Locally C -equivalent algebras. J. Funct. Anal. 23 (1976), 95106.Google Scholar
Cusack, J. M., Jordan derivations on rings. Proc. Amer. Math. Soc. 53 (1975), 321–4.Google Scholar
Dales, H. G., Norming nil algebras. Proc. Amer. Math. Soc. 83 (1981), 71–4.Google Scholar
Dales, H. G., On norms on algebras. In [773], pp. 61–96.Google Scholar
Dang, T., Real isometries between JB -triples. Proc. Amer. Math. Soc. 114 (1992), 971–80.Google Scholar
Dang, T. and Russo, B., Real Banach Jordan triples. Proc. Amer. Math. Soc. 122 (1994), 135–45.Google Scholar
Darpö, E. and Rochdi, A., Classification of the four-dimensional power-commutative real division algebras. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), 1207–23.Google Scholar
Davis, W. J., Separable Banach spaces with only trivial isometries. Rev. Roumaine Math. Pures Appl. 16 (1971), 1051–4.Google Scholar
Davis, W. J., Figiel, T., Johnson, W. B., and Pełczyński, A., Factoring weakly compact operators. J. Funct. Anal. 17 (1974), 311–27.Google Scholar
Diankha, O., Diouf, A., and Rochdi, A., A brief statement on the absolute-valued algebras with one-sided unit. Int. J. Algebra 7 (2013), 833–8.Google Scholar
Dickson, L. E., On quaternions and their generalization and the history of the eight square theorem. Ann. of Math. 20 (1919), 155–71.Google Scholar
Dickson, L. E., Linear algebras with associativity not assumed. Duke Math. J. 1 (1935), 113–25.Google Scholar
Dineen, S., The second dual of a JB -triple system. In Complex Analysis, Functional Analysis and Approximation Theory (ed. Múgica, J.), pp. 67–9, North-Holland Math. Stud. 125, North-Holland, Amsterdam–New York, 1986. xix, 2, 211, 236, 241Google Scholar
Doran, R. S., A generalization of a theorem of Civin and Yood on Banach ∗-algebras. Bull. London Math. Soc. 4 (1972), 25–6.Google Scholar
Dorofeev, G. V., An example of a solvable but not nilpotent alternative ring. Uspekhi Mat. Nauk 15 (1960), 147–50.Google Scholar
Duncan, J., Review of [425]. Math. Rev. 87e:46067.Google Scholar
Duncan, J., McGregor, C. M., Pryce, J. D., and White, A. J., The numerical index of a normed space. J. London Math. Soc. 2 (1970), 481–8.Google Scholar
Duncan, J. and Taylor, P. J., Norm inequalities for C -algebras. Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), 119–29. 400Google Scholar
Dunford, N., Spectral theory I. Convergence to projections. Trans. Amer. Math. Soc. 54 (1943), 185217.Google Scholar
Dutta, S. and Rao, T. S. S. R. K., Norm-to-weak upper semi-continuity of the pre-duality map. J. Anal. 12 (2005), 110.Google Scholar
Eakin, P. and Sathaye, A., On automorphisms and derivations of Cayley–Dickson algebras. J. Algebra 129 (1990), 263–78.Google Scholar
Edwards, C. M., On Jordan W -algebras. Bull. Sci. Math. 104 (1980), 393403. xix, xx, 2, 19Google Scholar
Edwards, C. M., Multipliers of JB-algebras. Math. Ann. 249 (1980), 265–72.Google Scholar
Edwards, C. M., Fernández-Polo, F. J., Hoskin, C. S., and Peralta, A. M., On the facial structure of the unit ball in a JB -triple. J. Reine Angew. Math. 641 (2010), 123–44.Google Scholar
Edwards, C. M. and Rüttimann, G. T., On the facial structure of the unit balls in a JBW -triple and its predual. J. London Math. Soc. 38 (1988), 317–32.Google Scholar
Edwards, C. M. and Rüttimann, G. T., The facial and inner ideal structure of a real JBW -triple. Math. Nachr. 222 (2001), 159–84.Google Scholar
Edwards, R. E., Multiplicative norms on Banach algebras. Math. Proc. Cambridge Phil. Soc. 47 (1951), 473–4.Google Scholar
Effros, E. G. and Størmer, E., Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc. 127 (1967), 313–16.Google Scholar
Effros, E. G. and Størmer, E., Positive projections and Jordan structure in operator algebras. Math. Scand. 45 (1979), 127–38. 210Google Scholar
Eidelheit, M., On isomorphisms of rings of linear operators. Studia Math. 9 (1940), 97105.Google Scholar
Eilenberg, S., Extensions of general algebras. Ann. Soc. Polon. Math. 21 (1948), 125–34.Google Scholar
Elduque, A. and Pérez, J. M., Infinite-dimensional quadratic forms admitting composition. Proc. Amer. Math. Soc. 125 (1997), 2207–16.Google Scholar
Ellis, A. J., The duality of partially ordered normed linear spaces. J. London Math. Soc. 39 (1964), 730–44.Google Scholar
Ellis, A. J., Minimal decompositions in base normed spaces. In Foundations of quantum mechanics and ordered linear spaces (Advanced Study Inst., Marburg, 1973), pp. 30–2. Lecture Notes in Phys. 29, Springer, Berlin, 1974.Google Scholar
El-Mallah, M. L., Quelques résultats sur les algèbres absolument valuées. Arch. Math. 38 (1982), 432–7.Google Scholar
El-Mallah, M. L., Sur les algèbres absolument valuées qui vérifient l’identité (x, x, x)=0. J. Algebra 80 (1983), 314–22.Google Scholar
El-Mallah, M. L., On finite dimensional absolute valued algebras satisfying (x, x, x)=0. Arch. Math. 49 (1987), 1622.Google Scholar
El-Mallah, M. L., Absolute valued algebras with an involution. Arch. Math. 51 (1988), 3949.Google Scholar
El-Mallah, M. L., Absolute valued algebras containing a central idempotent. J. Algebra 128 (1990), 180–7.Google Scholar
El-Mallah, M. L., Absolute valued algebraic algebra satisfying (x, x, x) = 0. Pure Math. Appl. 8 (1997), 3952.Google Scholar
El-Mallah, M. L., Semi-algebraic absolute valued algebras with an involution. Comm. Algebra 31 (2003), 3135–41.Google Scholar
El-Mallah, M. L., Elgendy, H., Rochdi, A., and Rodríguez, A., On absolute valued algebras with involution. Linear Algebra Appl. 414 (2006), 295303.Google Scholar
El-Mallah, M. L. and Micali, A., Sur les algèbres normées sans diviseurs topologiques de zéro. Bol. Soc. Mat. Mexicana 25 (1980), 23–8.Google Scholar
El-Mallah, M. L. and Micali, A., Sur les dimensions des algèbres absolument valuées. J. Algebra 68 (1981), 237–46.Google Scholar
Enflo, P., A counterexample to the approximation problem in Banach spaces. Acta Math. 130 (1973), 309–17.Google Scholar
Erickson, T. S., Martindale, W. S. III, and Osborn, J. M., Prime nonassociative algebras. Pacific J. Math. 60 (1975), 4963. 495Google Scholar
Esterle, J., Normes d’algèbres minimales, topologie d’algèbre normée minimum sur certaines algèbres d’endomorphismes continus d’un espace normé. C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A425–7.Google Scholar
Fan, K. and Glicksberg, I., Some geometrical properties of the spheres in a normed linear space. Duke Math. J. 25 (1958), 553–68.Google Scholar
Feldman, K. E., New proof of Frobenius hypothesis on the dimensions of real algebras without divisors of zero. Moscow Univ. Math. Bull. 55 (2000), 4850.Google Scholar
Fernández, A., Modular annihilator Jordan algebras. Comm. Algebra 13 (1985), 2597–613. 598Google Scholar
Fernández, A., Noncommutative Jordan Riesz algebras. Quart. J. Math. Oxford 39 (1988), 6780. 598, 599Google Scholar
Fernández, A., Noncommutative Jordan algebras containing minimal inner ideals. In [749], pp. 153–76.Google Scholar
Fernández, A., Banach–Lie algebras spanned by extremal elements. In [704], pp. 125–32. 598Google Scholar
Fernández, A., Banach–Lie algebras with extremal elements. Quart. J. Math. Oxford 62 (2011), 115–29. 598Google Scholar
Fernández, A., García, E., and Rodríguez, A., A Zel’manov prime theorem for JB -algebras. J. London Math. Soc. 46 (1992), 319–35. xxi, xxii, 405, 408, 437, 466, 467Google Scholar
Fernández, A., García, E., and Sánchez, E., von Neumann regular Jordan Banach triple systems. J. London Math. Soc. 42 (1990), 3248. 599, 600Google Scholar
Fernández, A. and Rodríguez, A., Primitive noncommutative Jordan algebras with nonzero socle. Proc. Amer. Math. Soc. 96 (1986), 199206. 598Google Scholar
Fernández, A. and Rodríguez, A., On the socle of a noncommutative Jordan algebra. Manuscripta Math. 56 (1986), 269–78. 598Google Scholar
Fernández, A. and Rodríguez, A., A Wedderburn theorem for nonassociative complete normed algebras. J. London Math. Soc. 33 (1986), 328–38. xxv, 548, 583, 584, 585Google Scholar
Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., Surjective isometries between real JB -triples. Math. Proc. Cambridge Phil. Soc. 137 (2004), 709–23.Google Scholar
Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., Geometric characterization of tripotents in real and complex JB -triples. J. Math. Anal. Appl. 295 (2004), 435–43.Google Scholar
Fernández-Polo, F. J., Garcés, J. J., and Peralta, A. M., A Kaplansky theorem for JB -triples. Proc. Amer. Math. Soc. 140 (2012), 3179–91.Google Scholar
Finet, C., Uniform convexity properties of norms on superreflexive Banach spaces. Israel J. Math. 53 (1986), 8192.Google Scholar
Foias, C., Sur certains theoremes de J. von Neumann concernant les ensembles spectraux. Acta Sci. Math. 18 (1957), 1520.Google Scholar
Ford, J. W. M., A square root lemma for Banach ∗-algebras. J. London Math. Soc. 42 (1967), 521–2.Google Scholar
Formanek, E., The Nagata–Higman Theorem. Acta Appl. Math. 21 (1990), 185–92.Google Scholar
Franchetti, C., Lipschitz maps and the geometry of the unit ball in normed spaces. Arch. Math. 46 (1986), 7684.Google Scholar
Franchetti, C. and Payá, R., Banach spaces with strongly subdifferentiable norm. Boll. Un. Mat. Ital. 7 (1993), 4570.Google Scholar
Friedman, Y. and Russo, B., Structure of the predual of a JBW -triple. J. Reine Angew. Math. 356 (1985), 6789. 236, 274, 332, 337Google Scholar
Friedman, Y. and Russo, B., The Gelfand–Naimark theorem for JB -triples. Duke Math. J. 53 (1986), 139–48. xxii, 459Google Scholar
Frobenius, F. G., Über lineare Substitutionen und bilineare Formen. J. Reine Angew. Math. 84 (1878), 163. Reprinted in Gesammelte Abhandlungen Band I, pp. 343–405.Google Scholar
Froelich, J., Unital multiplications on a Hilbert space. Proc. Amer. Math. Soc. 117 (1993), 757–9.Google Scholar
Fukamiya, M., On a theorem of Gelfand and Neumark and the B -algebra. Kumamoto J. Sci. Ser. A 1 (1952), 1722. 686Google Scholar
Fuster, R. and Marquina, A., Geometric series in incomplete normed algebras. Amer. Math. Monthly 91 (1984), 4951.Google Scholar
Galé, J. E., Weakly compact homomorphisms in nonassociative algebras. In [734], pp. 167–71.Google Scholar
Galé, J. E., Ransford, T. J., and White, M. C., Weakly compact homomorphisms. Trans. Amer. Math. Soc. 331 (1992), 815–24. 336Google Scholar
Galina, E., Kaplan, A., and Saal, L., Charged representations of the infinite Fermi and Clifford algebras. Lett. Math. Phys. 72 (2005), 6577.Google Scholar
Galina, E., Kaplan, A., and Saal, L., Spinor types in infinite dimensions. J. Lie Theory 15 (2005), 457–95.Google Scholar
Gantmacher, V., Über schwache totalstetige Operatoren. Rec. Math. [Mat. Sbornik] 7 (1940), 301–8.Google Scholar
Gardner, L. T., On isomorphisms of C -algebras. Amer. J. Math. 87 (1965), 384–96.Google Scholar
Gardner, L. T., An elementary proof of the Russo–Dye theorem. Proc. Amer. Math. Soc. 90 (1984), 181.Google Scholar
Garibaldi, S. and Petersson, H. P., Wild Pfister forms over Henselian fields, K-theory, and conic division algebras. J. Algebra 327 (2011), 386465.Google Scholar
Gelfand, I. M., Abstrakte Funktionen und lineare Operatoren, Mat. Sb. 4 (1938), 235–86.Google Scholar
Gelfand, I. M., Normierte Ringe. Rec. Math. [Mat. Sbornik]9 (1941), 324.Google Scholar
Gelfand, I. M. and Naimark, M. A., On the embedding of normed rings into the ring of operators in Hilbert space. Mat. Sbornik 12 (1943), 197213.Google Scholar
Gelfand, I. M. and Kolmogorov, A. N., Rings of continuous functions on topological spaces. Doklady Akad. Nauk SSSR 22 (1939), 1115.Google Scholar
Giles, J. R., Gregory, D. A., and Sims, B., Geometrical implications of upper semi-continuity of the duality mapping of a Banach space. Pacific J. Math. 79 (1978), 99109.Google Scholar
Gleichgewicht, B., A remark on absolute-valued algebras. Colloq. Math. 11 (1963), 2930.Google Scholar
Glickfeld, B. W., A metric characterization of C(X) and its generalization to C -algebras. Illinois J. Math. 10 (1966), 547–56.Google Scholar
Glimm, J. G. and Kadison, R. V., Unitary operators in C -algebras. Pacific J. Math. 10 (1960), 547–56.Google Scholar
Godefroy, G. and Indumathi, V., Norm-to-weak upper semi-continuity of the duality and pre-duality mappings. Set-Valued Anal. 10 (2002), 317–30.Google Scholar
Godefroy, G., Montesinos, V., and Zizler, V., Strong subdifferentiability of norms and geometry of Banach spaces. Comment. Math. Univ. Carolinae 36 (1995), 493502.Google Scholar
Godefroy, G. and Rao, T. S. S. R. K., Renorming and extremal structures. Illinois J. Math. 48 (2004), 1021–9.Google Scholar
Gohberg, I. C., Markus, A. S., and Fel’dman, I. A., Normally solvable operators and ideals associated with them. Bul. Akad. Stiince RSS Moldoven 10 (1960), 5170. Amer. Math. Soc. Transl. 61 (1967), 63–4.Google Scholar
Golod, E. S., On nil-algebras and finitely approximable p-groups. Izv. Akad. Nauk SSSR, Ser. Mat. 28 (1964), 273–6. 633Google Scholar
Gorin, E. A., Bernstein inequalities from the perspective of operator theory. (In Russian.) Vestnik Khar’kov. Gos. Univ. 205 (1980), 77105, 140.Google Scholar
Gowers, W. T. and Maurey, B., The unconditional basic sequence problem. J. Amer. Math. Soc. 6 (1993), 851–74.Google Scholar
Grabiner, S., The nilpotence of Banach nil algebras. Proc. Amer. Math. Soc. 21 (1969), 510.Google Scholar
Gregory, D. A., Upper semi-continuity of subdifferential mappings. Canad. Math. Bull. 23 (1980), 1119.Google Scholar
Greim, P. and Rajalopagan, M., Almost transitivity in C 0(L). Math. Proc. Cambridge Phil. Soc. 121 (1997), 7580.Google Scholar
Grzaślewicz, R. and Scherwentke, P., On strongly extreme and denting contractions in L (C(X), C(Y)). Bull. Acad. Sinica 25 (1997), 155–60.Google Scholar
Haagerup, U., Kadison, R. V., and Pedersen, G. K., Means of unitary operators, revisited. Math. Scand. 100 (2007), 193–7.Google Scholar
Haïly, A., A non-semiprime associative algebra with zero weak radical. Extracta Math. 12 (1997), 5360.Google Scholar
Haïly, A., Kaidi, A., and Rodríguez, A., Algebra descent spectrum of operators. Israel J. Math. 177 (2010), 349–68.Google Scholar
Hamana, M., Injective envelopes of C -algebras. J. Math. Soc. Japan 31 (1979), 181–97.Google Scholar
Hamilton, W. R., Note by Professor Sir W. R. Hamilton, respecting the researches of John T. Graves, esq. Trans. R. Irish Acad., 1848, Science 338–41.Google Scholar
Hammoudi, L., Nil-algebras and infinite groups. J. Math. Sci. (NY) 144 (2007), 4004–12.Google Scholar
Hanche-Olsen, H., A note on the bidual of a JB-algebra. Math. Z. 175 (1980), 2931.Google Scholar
Hansen, M. L. and Kadison, R. V., Banach algebras with unitary norms. Pacific J. Math. 175 (1996), 535–52.Google Scholar
Hansen, F. and Pedersen, G. K., Jensen’s inequality for operators and Löwner’s theorem. Math. Ann. 258 (1981/82), 229–41.Google Scholar
Harmand, P. and Rao, T. S. S. R. K., An intersection property of balls and relations with M-ideals. Math. Z. 197 (1988), 277–90.Google Scholar
Harris, L. A., The numerical range of holomorphic functions in Banach spaces. Amer. J. Math. 93 (1971), 1005–19.Google Scholar
Harris, L. A., Banach algebras with involution and Möbius transformations. J. Funct. Anal. 11 (1972), 116.Google Scholar
Harris, L. A., Bounded symmetric homogeneous domains in infinite dimensional spaces. In Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973), pp. 1340. Lecture Notes in Math. 364, Springer, Berlin, 1974. 210, 211Google Scholar
Harris, L. A., The numerical range of functions and best approximation. Math. Proc. Cambridge Philos. Soc. 76 (1974), 133–41.Google Scholar
Harris, L. A. and Kadison, R. V., Schurian algebras and spectral additivity. J. Algebra 180 (1996), 175–86.Google Scholar
Harte, R. and Mbekhta, M., On generalized inverses in C -algebras. Studia Math. 103 (1992), 71–7.Google Scholar
Heinrich, S., Ultraproducts in Banach space theory. J. Reine Angew. Math. 313 (1980), 72104. 211, 236Google Scholar
Hejazian, S. and Niknam, A., A Kaplansky theorem for JB -algebras. Rocky Mountain J. Math. 28 (1998), 977–82.Google Scholar
Herstein, I. N., Jordan homomorphism. Trans. Amer. Math. Soc. 81 (1956), 331–41.Google Scholar
Herstein, I. N., Jordan derivations of prime rings. Proc. Amer. Math. Soc. 8 (1957), 1104–10.Google Scholar
Hessenberger, G., A spectral characterization of the socle of Banach Jordan systems. Math. Z. 223 (1996), 561–8. 603Google Scholar
Hessenberger, G., Inessential and Riesz elements in Banach Jordan systems. Quart. J. Math. Oxford 47 (1996), 337–47. 603Google Scholar
Hessenberger, G., The trace in Banach Jordan pairs. Bull. London Math. Soc. 30 (1998), 561–8. 603Google Scholar
Hessenberger, G., An improved characterization of inessential elements in Banach Jordan systems and the generalized Ruston characterization. Arch. Math. (Basel) 74 (2000), 438–40. 603Google Scholar
Hessenberger, G. and Maouche, A., On Banach Jordan systems with at most two spectral values. Far East J. Math. Sci. (FJMS) 7 (2002), 115–20. 603Google Scholar
Hirschfeld, R. A. and Johnson, B. E., Spectral characterization of finite-dimensional algebras. Indag. Math. 34 (1972), 1923. 596Google Scholar
Hogben, L. and McCrimmon, K., Maximal modular inner ideals and the Jacobson radical of a Jordan algebra. J. Algebra 68 (1981), 155–69.Google Scholar
Holsztynski, W., Continuous mappings induced by isometries of spaces of continuous functions. Studia Math. 26 (1966), 133–6.Google Scholar
Horn, G., Classification of JBW -triples of Type I. Math. Z. 196 (1987), 271–91. xxii, 340, 344, 438, 459Google Scholar
Horn, G., Coordinatization theorem for JBW -triples. Quart. J. Math. Oxford 38 (1987), 321–35. xxi, 411, 416Google Scholar
Huang, X.-J. and Ng, C.-K., An abstract characterization of unital operator spaces. J. Operator Theory 67 (2012), 289–98.Google Scholar
Huruya, T., The normed space numerical index of C -algebras. Proc. Amer. Math. Soc. 63 (1977), 289–90.Google Scholar
Hurwitz, A., Über die Composition der quadratischen Formen von beliebig vielen Variabelm. Nach. Ges. Wiss. Göttingen (1898), 309–16.Google Scholar
Imaeda, K. and Imaeda, M., Sedenions: algebra and analysis. Appl. Math. Comp. 115 (2000), 7788.Google Scholar
Ingelstam, L., A vertex property for Banach algebras with identity, Math. Scand. 11 (1962), 2232.Google Scholar
Ingelstam, L., Hilbert algebras with identity. Bull. Amer. Math. Soc. 69 (1963), 794–6.Google Scholar
Ingelstam, L., Non-associative normed algebras and Hurwitz’ problem. Ark. Mat. 5 (1964), 231–8.Google Scholar
Ingelstam, L., Real Banach algebras. Ark. Mat. 5 (1964), 239–79.Google Scholar
Iochum, B., Loupias, G, and Rodríguez, A., Commutativity of C -algebras and associativity of JB -algebras. Math. Proc. Cambridge Phil. Soc. 106 (1989), 281–91. xxi, 398, 399, 400, 401Google Scholar
Isidro, J. M., Kaup, W., and Rodríguez, A., On real forms of JB -triples. Manuscripta Math. 86 (1995), 311–35. 242, 243, 459Google Scholar
Isidro, J. M. and Rodríguez, A., Isometries of JB-algebras. Manuscripta Math. 86 (1995), 337–48.Google Scholar
Isidro, J. M. and Rodríguez, A., On the definition of real W*-algebras. Proc. Amer. Math. Soc. 124 (1996), 3407–10. 244Google Scholar
Jacobson, N., Structure theory of simple rings without finiteness assumptions. Trans. Amer. Math. Soc. 57 (1945), 228–45.Google Scholar
Jacobson, N., The radical and semisimplicity for arbitrary rings. Amer. J. Math. 67 (1945), 300–20.Google Scholar
Jacobson, N., A topology for the set of primitive ideals in an arbitrary ring. Proc. Nat. Acad. Sci. USA 31 (1945), 333–8.Google Scholar
Jacobson, N., Structure theory for algebraic algebras of bounded degree. Ann. of Math. 46 (1945), 695707.Google Scholar
Jacobson, N., A theorem on the structure of Jordan algebras. Proc. Nat. Acad. Sci. USA 42 (1956), 140–7.Google Scholar
Jacobson, N., Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo 7 (1958), 5580.Google Scholar
Jacobson, N., Abraham Adrian Albert 1905–1972. Bull. Amer. Math. Soc. 80 (1974), 1075–100. Reprinted in [691], pp. xlv–lxiii. 546Google Scholar
Jacobson, N. and Rickart, C. E., Jordan homomorphisms of rings. Trans. Amer. Math. Soc. 69 (1950), 479502.Google Scholar
Johnson, B. E., Centralisers on certain topological algebras. J. London Math. Soc. 39 (1964), 603–14.Google Scholar
Johnson, B. E., The uniqueness of the (complete) norm topology. Bull. Amer. Math. Soc. 73 (1967), 537–9. 596Google Scholar
Johnson, B. E., Continuity of derivations on commutative Banach algebras. Amer. J. Math. 91 (1969), 110.Google Scholar
Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky. Amer. J. Math. 90 (1968), 1067–73. 466, 548, 596Google Scholar
Jordan, P., von Neumann, J., and Wigner, E., On an algebraic generalization of the quantum mechanical formalism. Ann. of Math. 35 (1934), 2964.Google Scholar
Kadets, V., Katkova, O., Martín, M., and Vishnyakova, A., Convexity around the unit of a Banach algebra. Serdica Math. J. 34 (2008), 619–28.Google Scholar
Kadison, R. V., Isometries of operator algebras. Ann. of Math. 54 (1951), 325–38.Google Scholar
Kadison, R. V., A generalized Schwarz inequality and algebraic invariants for operator algebras. Ann. of Math. 56 (1952), 494503.Google Scholar
Kadison, R. V. and Pedersen, G. K., Means and convex combinations of unitary operators. Math. Scand. 57 (1985), 249–66.Google Scholar
Kaidi, A., Structure des algèbres de Jordan–Banach non commutatives reelles de division. In [749], pp. 119–24. 597Google Scholar
Kaidi, A., Martínez, J., and Rodríguez, A., On a non-associative Vidav–Palmer theorem. Quart. J. Math. Oxford 32 (1981), 435–42.Google Scholar
Kaidi, A., Morales, A, and Rodríguez, A., Prime non-commutative JB -algebras. Bull. London Math. Soc. 32 (2000), 703–8. xxii, 421Google Scholar
Kaidi, A., Morales, A., and Rodríguez, A., Geometrical properties of the product of a C -algebra. Rocky Mountain J. Math. 31 (2001), 197213.Google Scholar
Kaidi, A., Morales, A, and Rodríguez, A., A holomorphic characterization of C - and JB -algebras. Manuscripta Math. 104 (2001), 467–78. xviii, 272, 273Google Scholar
Kaidi, A., Morales, A., and Rodríguez, A., Non-associative C -algebras revisited. In [1141], pp. 379–408. xx, 275, 330, 346, 421, 422Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Absolute-valued algebraic algebras are finite-dimensional. J. Algebra 195 (1997), 295307.Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Absolute-valued algebraic algebras. In [705], pp. 103–9.Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Nearly absolute-valued algebras. Comm. Algebra 30 (2002), 3267–84.Google Scholar
Kaidi, A. and Sánchez, A., J-diviseurs topologiques de zéro dans une algèbre de Jordan n.c. normée. In [733], pp. 193–7. 597Google Scholar
Kamowitz, H. and Scheinberg, S., The spectrum of automorphisms of Banach algebras. J. Funct. Anal. 4 (1969), 268–76.Google Scholar
Kaplansky, I., Topological rings. Amer. J. Math. 69 (1947), 153–83.Google Scholar
Kaplansky, I., Topological methods in valuation theory. Duke Math. J. 14 (1947), 527–41.Google Scholar
Kaplansky, I., Dual rings. Ann. of Math. 49 (1948), 689701. xxv, 551, 584Google Scholar
Kaplansky, I., Normed algebras. Duke Math. J. 16 (1949), 399418. 584Google Scholar
Kaplansky, I., Topological representation of algebras II. Trans. Amer. Math. Soc. 68 (1950), 6275.Google Scholar
Kaplansky, I., Infinite-dimensional quadratic forms permitting composition. Proc. Amer. Math. Soc. 4 (1953), 956–60. 360Google Scholar
Kaplansky, I., Ring isomorphisms of Banach algebras. Canad. J. Math. 6 (1954), 374–81. 596, 597Google Scholar
Kaplansky, I., ‘Problems in the theory of rings’ revisited. Amer. Math. Monthly 77 (1970), 445–54.Google Scholar
Kaup, W., Algebraic characterization of symmetric complex Banach manifolds. Math. Ann. 228 (1977), 3964. 2, 209, 210, 211, 241Google Scholar
Kaup, W., A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z. 183 (1983), 503–29. xix, 2, 209, 210, 211, 241Google Scholar
Kaup, W., Contractive projections on Jordan C -algebras and generalizations. Math. Scand. 54 (1984), 95100. xix, 207, 210Google Scholar
Kaup, W., On real Cartan factors. Manuscripta Math. 92 (1997), 191222. 460Google Scholar
Kaup, W., JB -triple. In [741], pp. 218–19. 462Google Scholar
Kaup, W. and Upmeier, H., Jordan algebras and symmetric Siegel domains in Banach spaces. Math. Z. 157 (1977), 179200. 211Google Scholar
Kawamura, K., On a conjecture of Wood. Glasgow Math. J. 47 (2005), 15.Google Scholar
Kelley, J. L. and Vaught, R. L., The positive cone in Banach algebras. Trans. Amer. Math. Soc. 74 (1953), 4455.Google Scholar
Kervaire, M., Non-parallelizability of the n sphere for n > 7. Proc. Nat. Acad. Sci. USA 44 (1958), 280–3.Google Scholar
Kleinecke, D. C., On operator commutators. Proc. Amer. Math. Soc. 8 (1957), 535–6.Google Scholar
Kleinfeld, E., Primitive alternative rings and semi-simplicity. Amer. J. Math. 77 (1955), 725–30. 570Google Scholar
Koliha, J. J., Isolated spectral points. Proc. Amer. Math. Soc. 124 (1996), 3417–24.Google Scholar
Koszmider, P., Martín, M., and Merí, J., Isometries on extremely non-complex Banach spaces. J. Inst. Math. Jussieu 10 (2011), 325–48.Google Scholar
Krupnik, N., Roch, S., and Silbermann, B., On C -algebras generated by idempotents. J. Funct. Anal. 137 (1996), 303–19.Google Scholar
Kulkarni, S. H., A very simple and elementary proof of a theorem of Ingelstam. Amer. Math. Monthly 111 (2004), 54–8.Google Scholar
Kunen, K. and Rosenthal, H., Martingale proofs of some geometrical results in Banach space theory. Pacific J. Math. 100 (1982), 153–75.Google Scholar
Kurosch, A., Ringtheoretische Probleme, die mit dem Burnsideschen Problem über periodische Gruppen in Zusammenhang stehen. Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 5 (1941), 233–40.Google Scholar
Kuwata, S., Born–Infeld Lagrangian using Cayley–Dickson algebras. Internat. J. Modern Physics A 19 (2004), 1525–48.Google Scholar
Laustsen, N. J., On ring-theoretic (in)finiteness of Banach algebras of operators on Banach spaces. Glasgow Math. J. 45 (2003), 1119.Google Scholar
Leung, C.-W., Ng, C.-K., and Wong, N.-C., Geometric unitaries in JB-algebras. J. Math. Anal. Appl. 360 (2009), 491–4.Google Scholar
Lima, Å., The metric approximation property, norm-one projections and intersection properties of balls. Israel J. Math. 84 (1993), 451–75.Google Scholar
Loos, O., Fitting decomposition in Jordan systems. J. Algebra 136 (1991), 92102.Google Scholar
Loos, O., Properly algebraic and spectrum-finite ideals in Jordan systems. Math. Proc. Cambridge Philos. Soc. 114 (1993), 149–61. 600Google Scholar
Loos, O., On the set of invertible elements in Banach Jordan algebras. Results Math. 29 (1996), 111–14. 597Google Scholar
Loos, O., Trace and norm for reduced elements of Jordan pairs. Comm. Algebra 25 (1997), 3011–42. 601Google Scholar
Loos, O., Nuclear elements in Banach Jordan pairs. In [705], pp. 111–17. 601Google Scholar
Loy, R. J., Maximal ideal spaces of Banach algebras of derivable elements. J. Austral. Math. Soc. 11 (1970), 310–12.Google Scholar
Lumer, G., Semi-inner-product spaces. Trans. Amer. Math. Soc. 100 (1961), 2943.Google Scholar
Lumer, G., Complex methods, and the estimation of operator norms and spectra from real numerical ranges. J. Funct. Anal. 10 (1972), 482–95.Google Scholar
Lumer, G. and Phillips, R. S., Dissipative operators in a Banach space. Pacific J. Math. 11 (1961), 679–98. 208Google Scholar
Macdonald, I. G., Jordan algebras with three generators. Proc. London Math. Soc. 10 (1960), 395408.Google Scholar
Magajna, B., Weak* continuous states on Banach algebras. J. Math. Anal. Appl. 350 (2009), 252–5.Google Scholar
Maouche, A., Caractérisations spectrales du radical et du socle d’une paire de Jordan–Banach. Canad. Math. Bull. 40 (1997), 488–97. 603Google Scholar
Maouche, A., Spectrum preserving linear mappings for scattered Jordan–Banach algebras. Proc. Amer. Math. Soc. 127 (1999), 3187–90. 603Google Scholar
Marcos, J. C., Rodríguez, A., and Velasco, M. V., A note on topological divisors of zero and division algebras. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 109 (2015), 93100.Google Scholar
Marcos, J. C. and Velasco, M. V., The Jacobson radical of a non-associative algebra and the uniqueness of the complete norm topology. Bull. London Math. Soc. 42 (2010), 1010–20.Google Scholar
Marcos, J. C. and Velasco, M. V., Continuity of homomorphisms into power-associative complete normed algebras. Forum Math. 25 (2013), 1109–25.Google Scholar
Martín, M., The group of isometries of a Banach space and duality. J. Funct. Anal. 255 (2008), 2966–76.Google Scholar
Martín, M. and Merí, J., Numerical index of some polyhedral norms on the plane. Linear Multilinear Algebra 55 (2007), 175–90.Google Scholar
Martín, M., Merí, J., and Payá, R., On the intrinsic and the spatial numerical range. J. Math. Anal. Appl. 318 (2006), 175–89.Google Scholar
Martín, M., Merí, J., and Rodríguez, A., Finite-dimensional Banach spaces with numerical index zero. Indiana Univ. Math. J. 53 (2004), 1279–89.Google Scholar
Martín, M. and Payá, R., Numerical index of vector-valued function spaces. Studia Math. 142 (2000), 269–80.Google Scholar
Martínez, J., JV-algebras. Math. Proc. Cambridge Philos. Soc. 87 (1980), 4750. 597Google Scholar
Martínez, J., Holomorphic functional calculus in Jordan–Banach algebras. In [749], pp. 125–34. 597Google Scholar
Martínez, J., Tracial elements for nonassociative H -algebras. In [733], pp. 257–68. xxv, 550Google Scholar
Martínez, J., Mena, J. F., Payá, R., and Rodríguez, A., An approach to numerical ranges without Banach algebra theory. Illinois J. Math. 29 (1985), 609–25. 673Google Scholar
Martínez, J. and Peralta, A. M., Separate weak-continuity of the triple product in dual real JB -triples. Math. Z. 234 (2000), 635–46. 243Google Scholar
Martínez, J. and Rodríguez, A., Imbedding elements whose numerical range has a vertex at zero in holomorphic semigroups. Proc. Edinburgh Math. Soc. 28 (1985), 91–5.Google Scholar
Mathieu, M., Rings of quotients of ultraprime Banach algebras, with applications to elementary operators. In [773], pp. 297–317. xxii, 408, 468, 547Google Scholar
Maurey, B., Banach spaces with few operators. In [757], pp. 1247–97.Google Scholar
Mazet, P., La preuve originale de S. Mazur pour son théorème sur les algèbres normées. Gaz. Math., Soc Math. Fr. 111 (2007), 511.Google Scholar
Mazur, S., Über konvexe Mengen in linearen normierten Räumen. Studia Math. 4 (1933), 7084.Google Scholar
Mazur, S., Sur les anneaux linéaires. C. R. Acad. Sci. Paris 207 (1938), 1025–7.Google Scholar
McCrimmon, K., Norms and noncommutative Jordan algebras. Pacific J. Math. 15 (1965), 925–56.Google Scholar
McCrimmon, K., Macdonald’s theorem with inverses. Pacific J. Math. 21 (1967), 315–25.Google Scholar
McCrimmon, K., The radical of a Jordan algebra. Proc. Nat. Acad. Sci. USA 62 (1969), 671–8. 597Google Scholar
McCrimmon, K., Noncommutative Jordan rings. Trans. Amer. Math. Soc. 158 (1971), 133. xxi, 273, 348, 411Google Scholar
McCrimmon, K. and Zel’manov, E., The structure of strongly prime quadratic Jordan algebras. Adv. Math. 69 (1988), 133222. xxi, 348, 365, 464Google Scholar
McGuigan, R., Strongly extreme points in Banach spaces. Manuscripta Math. 5 (1971), 113–22.Google Scholar
McIntosh, A., Functions and derivations of C -algebras. J. Funct. Anal. 30 (1978), 264–75.Google Scholar
Medbouhi, A. and Tajmouati, A., Calcul fonctionnel harmonique dans les algèbres de Banach alternatives involutives et applications. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), 141–52.Google Scholar
Mena, J. F. and Rodríguez, A., Weakly compact operators on non-complete normed spaces. Expo. Math. 27 (2009), 143–51.Google Scholar
Mena, J. F. and Rodríguez, A., Compact and weakly compact operators on non-complete normed spaces. In [704], pp. 205–11.Google Scholar
Meyberg, A., Identitäten und das Radikal in Jordan-Tripelsystemen. Math. Ann. 197 (1972), 203–20.Google Scholar
Milman, V. D., The infinite-dimensional geometry of the unit sphere of a Banach space. Soviet Math. Dokl. 8 (1967), 1440–4.Google Scholar
Milnor, J., Some consequences of a theorem of Bott. Ann. of Math. 68 (1958), 444–9.Google Scholar
Moore, R. T., Hermitian functionals on B-algebras and duality characterizations of C -algebras. Trans. Amer. Math. Soc. 162 (1971), 253–65.Google Scholar
Moreno, A., Distinguishing Jordan polynomials by means of a single Jordan-algebra norm. Studia Math. 122 (1997), 6773. xxii, 470Google Scholar
Moreno, A. and Rodríguez, A., On the Zel’manovian classification of prime JB -triples. J. Algebra 226 (2000), 577613. xxii, 422, 458, 460, 461Google Scholar
Moreno, A. and Rodríguez, A., On the Zel’manovian classification of prime JB - and JBW -triples. Comm. Algebra 31 (2003), 1301–28. xxii, 458, 459, 460, 461Google Scholar
Moreno, A. and Rodríguez, A., Introducing Analysis in Zel’manov’s theorems for Jordan systems. In Comptes Rendus de la Premièr Rencontre Maroco-Andalouse sur les Algèbres et leurs Applications, Tétouan, Septembre 2001, pp. 836, Université Abdelmalek Essaadi, Faculté des Sciences, Tétouan, 2003. 462Google Scholar
Moreno, A. and Rodríguez, A., A bilinear version of Holsztynski’s theorem on isometries of C(X)-spaces. Studia Math. 166 (2005), 8391.Google Scholar
Moreno, A. and Rodríguez, A., On multiplicatively closed subsets of normed algebras. J. Algebra 323 (2010), 1530–52. xxvi, 652, 653Google Scholar
Moreno, A. and Rodríguez, A., Topologically nilpotent normed algebras. J. Algebra 368 (2012), 126–68. xxvi, 652, 653, 654, 655, 656, 658Google Scholar
Moreno, G., The zero divisors of the Cayley–Dickson algebras over the real numbers. Bol. Soc. Mat. Mexicana 4 (1998), 1328.Google Scholar
Moreno, G., Alternative elements in the Cayley–Dickson algebras. In Topics in mathematical physics, general relativity and cosmology in honor of Jerzy Plebañski , pp. 333–46, World Sci. Publ., Hackensack, NJ, 2006.Google Scholar
Moutassim, A. and Rochdi, A., Sur les algèbres préhilbertiennes vérifiant ‖a 2‖ ≤‖a2 . Adv. appl. Clifford alg. 18 (2008), 269–78.Google Scholar
Nagumo, M., Einige analytishe Untersuchunger in linearen metrishen Ringen. Jap. J. Math. 13 (1936), 6180.Google Scholar
Nakamura, M., Complete continuities of linear operators. Proc. Japan Acad. 27 (1951), 544–7.Google Scholar
Navarro-Pascual, J. C. and Navarro, M. A., Unitary operators in real von Neumann algebras. J. Math. Anal. Appl. 386 (2012), 933–8.Google Scholar
Neher, E., Generators and relations for 3-graded Lie algebras, J. Algebra 155 (1993), 135. xxv, 554Google Scholar
von Neumann, J., On an algebraic generalization of the quantum mechanical formalism I. Mat. Sb. 1 (1936), 415–84.Google Scholar
Neumann, M. M., Rodríguez, A., and Velasco, M. V., Continuity of homomorphisms and derivations on algebras of vector-valued functions. Quart. J. Math. Oxford 50 (1999), 279300. 596, 709Google Scholar
Nieto, J. I., Normed right alternative algebras over the reals. Canad. J. Math. 24 (1972), 1183–6.Google Scholar
Nieto, J. I. Gateaux differentials in Banach algebras. Math. Z. 139 (1974), 2334.Google Scholar
Oja, E., On bounded approximation properties of Banach spaces. In Banach algebras 2009, pp. 219–31, Banach Center Publ. 91, Polish Acad. Sci. Inst. Math., Warsaw, 2010.Google Scholar
Okayasu, T., A structure theorem of automorphisms of von Neumann algebras. Tôhoku Math. J. 20 (1968), 199206.Google Scholar
Okubo, S., Pseudo-quaternion and pseudo-octonion algebras. Hadronic J. 1 (1978), 1250–78.Google Scholar
Okubo, S. and Osborn, J. M., Algebras with nondegenerate associative symmetric forms permitting composition. Comm. Algebra 9 (1981), 1233–61.Google Scholar
Olsen, C. L. and Pedersen, G. K., Convex combinations of unitary operators in von Neumann algebras. J. Funct. Anal. 66 (1986), 365–80.Google Scholar
Osborn, J. M., Quadratic division algebras. Trans. Amer. Math. Soc. 105 (1962), 202–21.Google Scholar
Osborn, J. M., Varieties of algebras. Adv. Math. 8 (1972), 163369.Google Scholar
Ostrowski, A., Über einige Lösungen der Funktionalgleichung Ψ(x)Ψ(y) = Ψ(xy). Acta Math. 41 (1918), 271–84.Google Scholar
Palais, R. S., The classification of real division algebras. Amer. Math. Monthly 75 (1968), 366–8.Google Scholar
Palmer, T. W., Characterizations of C -algebras. Bull. Amer. Math. Soc. 74 (1968), 538–40.Google Scholar
Palmer, T. W., Unbounded normal operators on Banach spaces. Trans. Amer. Math. Soc. 133 (1968), 385414.Google Scholar
Palmer, T. W., Characterizations of C -algebras II. Trans. Amer. Math. Soc. 148 (1970), 577–88.Google Scholar
Palmer, T. W., Real C -algebras. Pacific J. Math. 35 (1970), 195204.Google Scholar
Palmer, T. W., Spectral algebras. Rocky Mountain J. Math. 22 (1992), 293328.Google Scholar
Paterson, A. L. T., Isometries between B -algebras. Proc. Amer. Math. Soc. 22 (1969), 570–2.Google Scholar
Paterson, A. L. T. and Sinclair, A. M., Characterization of isometries between C -algebras. J. London Math. Soc. 5 (1972), 755–61.Google Scholar
Payá, R., Pérez, J., and Rodríguez, A., Non-commutative Jordan C -algebras. Manuscripta Math. 37 (1982), 87120. xx, xxi, 3, 19, 398, 411, 421Google Scholar
Payá, R., Pérez, J., and Rodríguez, A., Type I factor representations of non-commutative JB -algebras. Proc. London Math. Soc. 48 (1984), 428–44. xx, xxi, 398, 411, 421Google Scholar
Pedersen, G. K., Measure theory in C -algebras II. Math. Scand. 22 (1968), 6374.Google Scholar
Pedersen, G. K., The λ-function in operator algebras. J. Operator Theory 26 (1991), 345–81.Google Scholar
Peralta, A. M., On the axiomatic definition of real JB -triples. Math. Nachr. 256 (2003), 100–6.Google Scholar
Peralta, A. M., Positive definite hermitian mappings associated to tripotent elements. Expo. Math. 33 (2015), 252–8.Google Scholar
Peresi, L. A., Other nonassociative algebras. In The concise handbook of algebra (eds. Mikhalev, A. V. and Pilz, G. F.), pp. 343–7, Dordrecht, Kluwer Academic, 2002.Google Scholar
Pérez, J., Rico, L., and Rodríguez, A., Full subalgebras of Jordan–Banach algebras and algebra norms on JB -algebras. Proc. Amer. Math. Soc. 121 (1994), 1133–43. 336, 597Google Scholar
Pérez, J., Rico, L., Rodríguez, A., and Villena, A. R., Prime Jordan–Banach algebras with nonzero socle. Comm. Algebra 20 (1992), 1753. 598Google Scholar
Perlis, S., A characterization of the radical of an algebra. Bull. Amer. Math. Soc. 48 (1942), 128–32.Google Scholar
Phelps, R. R., Extreme points in function algebras. Duke Math. J. 32 (1965), 267–77.Google Scholar
Popa, S., On the Russo–Dye theorem. Michigan Math. J. 28 (1981), 311–15.Google Scholar
Pták, V., On the spectral radius in Banach algebras with involution. Bull. London Math. Soc. 2 (1970), 327–34.Google Scholar
Pták, V., Banach algebras with involution. Manuscripta Math. 6 (1972), 245–90.Google Scholar
Putter, P. S. and Yood, B., Banach Jordan ∗-algebras. Proc. London Math. Soc. 41 (1980), 2144. 597Google Scholar
Raeburn, I. and Sinclair, A. M., The C -algebra generated by two projections. Math. Scand. 65 (1989), 278–90.Google Scholar
Raffin, R., Anneaux a puissances commutatives and anneaux flexibles. C. R. Acad. Sci. Paris 230 (1950), 804–6.Google Scholar
Rambla, F., A counterexample to Wood’s conjecture. J. Math. Anal. Appl. 317 (2006), 659–67.Google Scholar
Ransford, T. J., A short proof of Johnson’s uniqueness-of-norm theorem. Bull. London Math. Soc. 21 (1989), 487–8.Google Scholar
Rickart, C. E., The singular elements of a Banach algebra. Duke Math. J. 14 (1947), 1063–77.Google Scholar
Rickart, C. E., The uniqueness of norm problem in Banach algebras. Ann. of Math. 51 (1950), 615–28.Google Scholar
Rickart, C. E., On spectral permanence for certain Banach algebras. Proc. Amer. Math. Soc. 4 (1953), 191–6.Google Scholar
Rickart, C. E., An elementary proof of a fundamental theorem in the theory of Banach algebras. Michigan Math. J. 5 (1958), 75–8.Google Scholar
Riesz, F., Sur certains systèmes singuliers d’équations intégrales. Ann. Sci. École Norm. Sup. 28 (1911), 3362.Google Scholar
Riesz, F., Über lineare Funktionalgleichungen. Acta Math. 41 (1916), 7198.Google Scholar
Robertson, A. G., A note on the unit ball in C -algebras. Bull. London Math. Soc. 6 (1974), 333–5.Google Scholar
Robertson, A. G. and Youngson, M. A., Positive projections with contractive complements on Jordan algebras. J. London Math. Soc. 25 (1982), 365–74. 210Google Scholar
Rochdi, A., Eight-dimensional real absolute valued algebras with left unit whose automorphism group is trivial. Int. J. Math. Math. Sci. 70 (2003), 4447–54.Google Scholar
Rochdi, A. and Rodríguez, A., Absolute valued algebras with involution. Comm. Algebra 37 (2009), 1151–9.Google Scholar
Rodríguez, A., Algebras estelares de Banach con elemento unidad. In Actas de las I Jornadas Matemáticas Hispano-Lusitanas, pp. 189210, Madrid, 1973.Google Scholar
Rodríguez, A., Derivaciones en álgebras normadas y commutatividad. Cuadernos del Dpto. de Estadística Matemática (Granada) 2 (1975), 5168.Google Scholar
Rodríguez, A., Teorema de estructura de los Jordan-isomorfismos de las C -álgebras. Rev. Mat. Hispano-Americana 37 (1977), 114–28.Google Scholar
Rodríguez, A., Rango numérico y derivaciones cerradas de las álgebras de Banach. In V Jornadas luso-espanholas de matemáticas, pp. 179200, Aveiro, 1978.Google Scholar
Rodríguez, A., A Vidav–Palmer theorem for Jordan C -algebras and related topics. J. London Math. Soc. 22 (1980), 318–32.Google Scholar
Rodríguez, A., Non-associative normed algebras spanned by hermitian elements. Proc. London Math. Soc. 47 (1983), 258–74. 210Google Scholar
Rodríguez, A., The uniqueness of the complete algebra norm topology in complete normed nonassociative algebras. J. Funct. Anal. 60 (1985), 115. 548, 597Google Scholar
Rodríguez, A., Mutations of C -algebras and quasiassociative JB -algebras. Collectanea Math. 38 (1987), 131–5.Google Scholar
Rodríguez, A., Jordan axioms for C -algebras. Manuscripta Math. 61 (1988), 279314. xxiv, 474, 549Google Scholar
Rodríguez, A., Automatic continuity with application to C -algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 345–7.Google Scholar
Rodríguez, A., An approach to Jordan–Banach algebras from the theory of nonassociative complete normed algebras. In [749], pp. 1–57. 584, 585, 586Google Scholar
Rodríguez, A., One-sided division absolute valued algebras. Publ. Mat. 36 (1992), 925–54.Google Scholar
Rodríguez, A., Closed derivations of Banach algebras. In Homenaje a Pablo Bobillo Guerrero, pp. 21–8, Univ. Granada, Granada, 1992.Google Scholar
Rodríguez, A., Primitive nonassociative normed algebras and extended centroid. In [734], pp. 233–43. 408, 601, 602Google Scholar
Rodríguez, A., Absolute valued algebras of degree two. In [733], pp. 350–6.Google Scholar
Rodríguez, A., Jordan structures in Analysis. In [764], pp. 97–186. xxii, 338, 340, 408, 462, 467, 549, 550, 553, 597, 601Google Scholar
Rodríguez, A., Continuity of densely valued homomorphisms into H -algebras. Quart . J. Math. Oxford 46 (1995), 107–18. xxiv, 546, 548, 549Google Scholar
Rodríguez, A., Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces. In Encuentro de Análisis Matemático, Homenaje al profesor B. Rodríguez-Salinas (eds. Bombal, F., Hernández, F. L., Jiménez y, P. de María, J. L.), Rev. Mat. Univ. Complutense Madrid 9 (1996), 149–89.Google Scholar
Rodríguez, A., Isometries and Jordan isomorphisms onto C -algebras. J. Operator Theory 40 (1998), 7185. 274, 346Google Scholar
Rodríguez, A., Continuity of homomorphisms into normed algebras without topological divisors of zero. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 94 (2000), 505–14. xxv, 595Google Scholar
Rodríguez, A., Sobre el tamaño de los conjuntos de números. In Actas del Encuentro de Matemáticos Andaluces, Sevilla 2000, Volumen I, pp. 235–48, Secretariado de Publicaciones de la Universidad de Sevilla, Sevilla, 2001.Google Scholar
Rodríguez, A., A numerical range characterization of uniformly smooth Banach spaces. Proc. Amer. Math. Soc. 129 (2001), 815–21.Google Scholar
Rodríguez, A., Banach–Jordan algebra. In [741], pp. 55–7. 462Google Scholar
Rodríguez, A., Absolute-valued algebras, and absolute-valuable Banach spaces. In Advanced Courses of Mathematical Analysis I, Proceedings of the First International School Cádiz, Spain 22–27 September 2002 (eds. Aizpuru-Tomás, A. and León-Saavedra, F.), pp. 99155, World Scientific, 2004.Google Scholar
Rodríguez, A., Numerical ranges of uniformly continuous functions on the unit sphere of a Banach space. J. Math. Anal. Appl. 297 (2004), 472–6. 208Google Scholar
Rodríguez, A., On Urbanik’s axioms for absolute valued algebras with involution. Comm. Algebra 36 (2008), 2588–92.Google Scholar
Rodríguez, A., Banach space characterizations of unitaries: a survey. J. Math. Anal. Appl. 369 (2010), 168–78.Google Scholar
Rodríguez, A., Approximately norm-unital products on C -algebras, and a nonassociative Gelfand–Naimark theorem. J. Algebra 347 (2011), 224–46. 421Google Scholar
Rodríguez, A., Slinko, A. M., and Zel’manov, E. I., Extending the norm from Jordan– Banach algebras of hermitian elements to their associative envelopes. Comm. Algebra 22 (1994), 1435–55. xxii, xxiii, 437, 470, 471, 472Google Scholar
Rodríguez, A. and Velasco, M. V., Continuity of homomorphisms and derivations on Banach algebras with an involution. In Function Spaces; Proceedings of the Third Conference on Function Spaces, May 19–23, 1998, Southern Illinois University at Edwardsville (ed. Jarosz, K.), pp. 289–98, Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999. xxii, 474, 475Google Scholar
Rodríguez, A. and Velasco, M. V., A non-associative Rickart’s dense-range-homomorphism theorem. Quart. J. Math. Oxford 54 (2003), 367–76. 597Google Scholar
Rordam, M., Advances in the theory of unitary rank and regular approximation. Ann. of Math. 128 (1988), 153–72.Google Scholar
Rosenthal, H., The Lie algebra of a Banach space. In Banach Spaces, pp. 129–57, Lecture Notes in Math. 1166, 1985.Google Scholar
Rosenthal, H., Functional Hilbertian sums. Pacific J. Math. 124 (1986), 417–67.Google Scholar
Rota, G.-C. and Strang, W. G., A note on the joint spectral radius. Indag. Math. 22 (1960), 379–81. xxvi, 650Google Scholar
Rowen, L. H., A short proof of the Chevalley–Jacobson density theorem, and a generalization. Amer. Math. Monthly 85 (1978), 185–6.Google Scholar
Ruan, Z.-J., Subspaces of C*-algebras. J. Funct. Anal. 76 (1988), 217–30.Google Scholar
Russo, B., Structure of JB -triples. In [764], pp. 209–80.Google Scholar
Russo, B. and Dye, H. A., A note on unitary operators in C -algebras. Duke Math. J. 33 (1966), 413–16.Google Scholar
Sakai, S., On a conjecture of Kaplansky. Tôhoku Math. J. 12 (1960), 31–3.Google Scholar
Sasiada, E. and Cohn, P. M., An example of a simple radical ring. J. Algebra 5 (1967), 373–7. 659Google Scholar
Schafer, R. D., On the algebras formed by the Cayley–Dickson process. Amer. J. Math. 76 (1954), 435–46.Google Scholar
Schafer, R. D., Noncommutative Jordan algebras of characteristic 0. Proc. Amer. Math. Soc. 6 (1955), 472–5.Google Scholar
Schafer, R. D., Generalized standard algebras. J. Algebra 12 (1969), 386417. 657Google Scholar
Schatz, J. A., Review of [273]. Math. Rev. 14 (1953), 884.Google Scholar
Schauder, J., Über lineare, vollstetige Funktionaloperationen. Studia Math. 2 (1930), 183–96.Google Scholar
Schoenberg, I. J., A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal. Proc. Amer. Math. Soc. 3 (1952), 961–4.Google Scholar
Schue, J. R., Hilbert space methods in the theory of Lie algebras, Trans. Amer. Math. Soc. 95 (1960), 6980. 553, 554Google Scholar
Schue, J. R., Cartan decompositions for L -algebras. Trans. Amer. Math. Soc. 98 (1961), 334–49. 553Google Scholar
Schur, 1. I., Neue Begründung der Theorie der Gruppencharaktere. Sitzungsberichte der Preuβischen Akademie der Wissenschaften 1905 Physik-Math. Klasse 406–32. Reprinted in Gesammelte Abhandlungen Vol. I pp. 143–69, Spriger, Berlin, 1973.Google Scholar
Segal, I. E., Irreducible representations of operator algebras. Bull. Amer. Math. Soc. 53 (1947), 7388.Google Scholar
Segre, B., La teoria delle algebre ed alcune questione di realtà. Univ. Roma, Ist. Naz. Alta. Mat., Rend. Mat. e Appl., serie 5 13 (1954), 157–88.Google Scholar
Shelah, S. and Steprans, J., A Banach space on which there are few operators. Proc. Amer. Math. Soc. 104 (1988), 101–5.Google Scholar
Sherman, D., A new proof of the noncommutative Banach–Stone theorem. Quantum probability , 363–75, Banach Center Publ. 73, Polish Acad. Sci. Inst. Math., Warsaw, 2006.Google Scholar
Shilov, G., On the extension of maximal ideals. C. R. (Doklady) Acad. Sci. URSS 29 (1940), 83–4.Google Scholar
Shirali, S. and Ford, J. W. M., Symmetry in complex involutory Banach algebras. II. Duke Math. J. 37 (1970), 275–80.Google Scholar
Shirokov, F. V., Proof of a conjecture by Kaplansky. (In Russian.) Uspekhi Mat. Nauk 11 (1956) 167–8.Google Scholar
Shirshov, A. I., On special J-rings. (In Russian.) Mat. Sb. 38 (80) (1956), 149–66.Google Scholar
Shirshov, A. I., On some non-associative nil-rings and algebraic algebras. Mat. Sb. 41 (83) (1957), 381–94.Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Joint spectral radius, operator semigroups, and a problem of W. Wojtynski. J. Funct. Anal. 177 (2000), 383441. xxvi, 652, 653, 654, 656Google Scholar
Shultz, F. W., On normed Jordan algebras which are Banach dual spaces. J. Funct. Anal. 31 (1979), 360–76. 19, 398, 401Google Scholar
Siddiqui, A. A., Self-adjointness in unitary isotopes of JB -algebras. Arch. Math. 87 (2006), 350–8.Google Scholar
Siddiqui, A. A., Asymmetric decompositions of vectors in JB -algebras. Arch. Math. (Brno) 42 (2006), 159–66.Google Scholar
Siddiqui, A. A., JB -algebras of topological stable rank 1. Int. J. Math. Math. Sci. 2007, Art. ID 37186, 24 pp.Google Scholar
Siddiqui, A. A., A proof of the Russo–Dye theorem for JB -algebras. New York J. Math. 16 (2010), 5360.Google Scholar
Siddiqui, A. A., Convex combinations of unitaries in JB -algebras. New York J. Math. 17 (2011), 127–37.Google Scholar
Siddiqui, A. A., The λ u -function in JB -algebras. New York J. Math. 17 (2011), 139–47.Google Scholar
Sinclair, A. M., Jordan automorphisms on a semisimple Banach algebra. Proc. Amer. Math. Soc. 25 (1970), 526–8.Google Scholar
Sinclair, A. M., Jordan homomorphisms and derivations on semisimple Banach algebras. Proc. Amer. Math. Soc. 24 (1970), 209–14.Google Scholar
Sinclair, A. M., The states of a Banach algebra generate the dual. Proc. Edinburgh Math. Soc. 17 (1970/71), 341–4.Google Scholar
Sinclair, A. M., The norm of a hermitian element in a Banach algebra. Proc. Amer. Math. Soc. 28 (1971), 446–50.Google Scholar
Sinclair, A. M., The Banach algebra generated by a derivation. In Spectral theory of linear operators and related topics (Timisoara/Herculane, 1983), pp. 241–50, Oper. Theory Adv. Appl. 14, Birkhäuser, Basel, 1984.Google Scholar
Singer, I. M. and Wermer, J., Derivations on commutative normed algebras. Math. Ann. 129 (1955), 260–4.Google Scholar
Skorik, A. and Zaidenberg, M., On isometric reflexions in Banach spaces. Math. Physics, Analysis, Geometry 4 (1997), 212–47.Google Scholar
Skosyrskii, V. G., Strongly prime noncommutative Jordan algebras. (In Russian.) Trudy Inst. Mat. (Novosibirk) 16 (1989), 131–64, Issled. po Teor. Kolets i Algebr, 198–9. 411, 422Google Scholar
Skosyrskii, V. G., Primitive Jordan algebras. Algebra Logic 31 (1993), 110–20. xxii, 462Google Scholar
Slinko, A. M., Complete metric Jordan algebras. Mat. Zametki 447 (1990), 100–5. English translation: Math. Notes 47 (1990), 491–4. 597Google Scholar
Slinko, A. M., 1, 2, 4, 8, … What comes next? Extracta Math. 19 (2004), 155–61.Google Scholar
Smiley, M. F., The radical of an alternative ring. Ann. of Math. 49 (1948), 702–9.Google Scholar
Smiley, M. F., Right H -algebras. Proc. Amer. Math. Soc. 4 (1953), 14.Google Scholar
Smiley, M. F., Real Hilbert algebras with identity. Proc. Amer. Math. Soc. 16 (1965) 440–1.Google Scholar
Smith, R. R., On Banach algebra elements of thin numerical range. Math. Proc. Cambridge Philos. Soc. 86 (1979), 7183.Google Scholar
Smith, R. R., The numerical range in the second dual of a Banach algebra. Math. Proc. Cambridge Philos. Soc. 89 (1981), 301–7.Google Scholar
Šmulyan, V., Sur la structure de la sphère unitaire dans l’espace de Banach. Math. Sb. 9 (1941), 545–61.Google Scholar
Spatz, I. N., Smooth Banach algebras. Proc. Amer. Math. Soc. 22 (1969), 328–9.Google Scholar
Spitkovsky, I., Once more on algebras generated by two projections. Linear Algebra Appl. 208 / 209 (1994), 377–95.Google Scholar
Spurný, J., A note on compact operators on normed linear spaces. Expo. Math. 25 (2007), 261–3.Google Scholar
Stachó, L. L., A projection principle concerning biholomorphic automorphisms. Acta Sci. Math. (Szeged) 44 (1982), 99124. xix, 207, 210Google Scholar
Steen, S. W. P., Introduction to the theory of operators. V. Metric rings, Proc. Cambridge Philos. Soc. 36 (1940), 139–49. 550Google Scholar
Stinespring, W. F., Positive functions on C -algebras. Proc. Amer. Math. Soc. 6, (1955), 211–16.Google Scholar
Stone, M. H., Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41 (1937), 375481.Google Scholar
Størmer, E., On the Jordan structure of C -algebras. Trans. Amer. Math. Soc. 120 (1965), 438–47.Google Scholar
Størmer, E., Jordan algebras of type I. Acta Math. 115 (1966), 165–84. 339Google Scholar
Størmer, E., Irreducible Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc. 130 (1968), 153–66. 339Google Scholar
Strasek, R. and Zalar, B., Uniform primeness of classical Banach Lie algebras of compact operators. Publ. Math. Debrecen 61 (2002), 325–40.Google Scholar
Strzelecki, E., Metric properties of normed algebras. Studia Math. 23 (1963), 4151.Google Scholar
Strzelecki, E., Power-associative regular real normed algebras. J. Austral. Math. Soc. 6 (1966), 193209.Google Scholar
Suttles, D., A counterexample to a conjecture of Albert. Notices Amer. Math. Soc., 19 (1972), A-566.Google Scholar
Szankowski, A., B(H) does not have the approximation property. Acta Math. 147 (1981), 89108.Google Scholar
Talponen, J., A note on the class of superreflexive almost transitive Banach spaces. Extracta Math. 23 (2008), 16.Google Scholar
Terekhin, P. A., Trigonometric algebras. J. Math. Sci. (New York) 95 (1999), 2156–60.Google Scholar
Thomas, M. P., The image of a derivation is contained in the radical. Ann. of Math. 128 (1988), 435–60.Google Scholar
Thomas, M. P., Primitive ideals and derivations on noncommutative Banach algebras. Pacific J. Math. 159 (1993), 139–52.Google Scholar
Toeplitz, O., Das algebraische Analogon zu einem Satze von Fejer. Math. Z. 2 (1918), 187–97.Google Scholar
Topping, D. M., An isomorphism invariant for spin factors. J. Math. Mech. 15 (1966), 1055–63.Google Scholar
Turovskii, Yu. V., On spectral properties of Lie subalgebras and on the spectral radius of subsets of a Banach algebra. (In Russian.) Spectral theory of operators and its applications, 6 (1985), 144–81. xxvi, 651Google Scholar
Uchiyama, M., Operator monotone functions which are defined implicitly and operator inequalities. J. Funct. Anal. 175 (2000), 330–47.Google Scholar
Urbanik, K., Absolute valued algebras with an involution. Fundamenta Math. 49 (1961), 247–58.Google Scholar
Urbanik, K., Remarks on ordered absolute valued algebras. Colloq. Math. 11 (1963), 31–9.Google Scholar
Urbanik, K. and Wright, F. B., Absolute valued algebras. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 285–6.Google Scholar
Urbanik, K. and Wright, F. B., Absolute valued algebras. Proc. Amer. Math. Soc. 11 (1960), 861–6.Google Scholar
Velasco, M. V., Spectral theory for non-associative complete normed algebras and automatic continuity. J. Math. Anal. Appl. 351 (2009), 97106.Google Scholar
Vesentini, E., On the subharmonicity of the spectral radius. Boll. Un. Mat. Ital. 1 (1968), 427–9.Google Scholar
Vidav, I., Eine metrische Kennzeichnung der selbstadjungierten Operatoren. Math. Z. 66 (1956), 121–8.Google Scholar
Villena, A. R., Continuity of derivations on H -algebras. Proc. Amer. Math. Soc. 122 (1994), 821–6. xxiv, 548, 549Google Scholar
Villena, A. R., Derivations on Jordan–Banach algebras. Studia Math. 118 (1996), 205–29. 466, 548Google Scholar
Villena, A. R., Automatic continuity in associative and nonassociative context. Irish Math. Soc. Bulletin 46 (2001), 4376.Google Scholar
Villena, A. R., Epimorphisms onto derivation algebras. Proc. Edinburgh Math. Soc. 46 (2003), 379–82.Google Scholar
Viola Devapakkiam, C., Jordan algebras with continuous inverse. Math. Japon. 16 (1971), 115–25. 597Google Scholar
Vowden, B. J., On the Gelfand–Neumark theorem. J. London Math. Soc. 42 (1967), 725–31.Google Scholar
Walsh, B., Classroom notes: The scarcity of cross products on Euclidean spaces. Amer. Math. Monthly 74 (1967), 188–94.Google Scholar
Wark, H. M., A non-separable reflexive Banach space on which there are few operators. J. London Math. Soc. 64 (2001), 675–89.Google Scholar
Wichmann, J., Hermitian ∗-algebras which are not symmetric. J. London Math. Soc. 8 (1974), 109–12.Google Scholar
Wichmann, J., On commutative B -equivalent algebras. Notices Amer. Math. Soc. (1975), Abstract 720–46–19.Google Scholar
Wichmann, J., The symmetric radical of an algebra with involution. Arch. Math. (Basel) 30 (1978), 83–8.Google Scholar
Wilansky, A., Letter to the Editor. Amer. Math. Monthly 91 (1984), 531.Google Scholar
Wilkins, T. J. D., Inessential ideals in Jordan–Banach algebras. Bull. London Math. Soc. 29 (1997), 7381. 603Google Scholar
Wojtaszczyk, P., Some remarks on the Daugavet equation. Proc. Amer. Math. Soc. 115 (1992), 1047–52.Google Scholar
Wood, G. V., Maximal symmetry in Banach spaces. Proc. Royal Irish Acad. 82A (1982), 177–86.Google Scholar
Wood, G. V., Maximal algebra norms. In Trends in Banach spaces and operator theory (Memphis, TN, 2001), pp. 335–45, Contemp. Math. 321, Amer. Math. Soc., Providence, RI, 2003.Google Scholar
Wright, F. B., Absolute valued algebras. Proc. Nat. Acad. Sci. USA 39 (1953), 330–2.Google Scholar
Wright, J. D. M., Jordan C -algebras. Michigan Math. J. 24 (1977), 291302. xx, 347, 398, 401Google Scholar
Wright, J. D. M. and Youngson, M. A., A Russo Dye theorem for Jordan C -algebras. In Functional analysis: surveys and recent results (Proc. Conf., Paderborn, 1976) (eds. Bierstedt, K. D. and Fuchssteiner, F.), pp. 279–82, North-Holland Math. Stud. 27, North-Holland, Amsterdam, 1977.Google Scholar
Wright, J. D. M. and Youngson, M. A., On isometries of Jordan algebras. J. London Math. Soc. 17 (1978), 339–44.Google Scholar
Wu, W., Locally pre-C -equivalent algebras. Proc. Amer. Math. Soc. 131 (2003), 555–62.Google Scholar
Yood, B., Topological properties of homomorphisms between Banach algebras. Amer. J. Math. 76 (1954), 155–67.Google Scholar
Yood, B., Homomorphisms on normed algebras. Pacific J. Math. 8 (1958), 373–81.Google Scholar
Yood, B., Faithful ∗-representations of normed algebras. Pacific J. Math. 10 (1960), 345–63.Google Scholar
Yood, B., Ideals in topological rings. Canad. J. Math. 16 (1964), 2845.Google Scholar
Yood, B., On axioms for B -algebras. Bull. Amer. Math. Soc. 76 (1970), 80–2.Google Scholar
Yost, D., A base norm space whose cone is not 1-generating. Glasgow Math. J. 25 (1984), 35–6. 690Google Scholar
Yost, D., Review of [650]. Zbl. Mat. 0544.46014.Google Scholar
Youngson, M. A., A Vidav theorem for Banach Jordan algebras. Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–72.Google Scholar
Youngson, M. A., Equivalent norms on Banach Jordan algebras. Math. Proc. Cambridge Philos. Soc. 86 (1979), 261–9. 597Google Scholar
Youngson, M. A., Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. 22 (1979), 93104.Google Scholar
Youngson, M. A., Nonunital Banach Jordan algebras and C -triple systems. Proc. Edinburgh Math. Soc. 24 (1981), 1929. 210Google Scholar
Zalar, B., Inner product characterizations of classical Cayley–Dickson algebras. In [733], pp. 405–9.Google Scholar
Zalar, B., On Hilbert spaces with unital multiplication. Proc. Amer. Math. Soc. 123 (1995), 1497–501.Google Scholar
Zalduendo, I., A simple example of a noncommutative Arens product. Publ. Mat. 35 (1991), 475–7.Google Scholar
Zelazko, W., On generalized topological divisors of zero in real m-convex algebras. Studia Math. 28 (1966/1967), 241–4.Google Scholar
Zeller-Meier, G., Sur les automorphismes des algèbres de Banach. C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A1131–2.Google Scholar
Zel’manov, E. I., Absolute zero-divisors and algebraic Jordan algebras. Siberian Math. J. 23 (1982), 841–54. 600Google Scholar
Zel’manov, E. I., On prime Jordan algebras II. Siberian Math. J. 24 (1983), 89104. xxi, 348, 364, 365, 366, 367, 401, 437Google Scholar
Zel’manov, E. I., On prime Jordan triple systems III. Siberian Math. J. 26 (1985), 7182. xxii, 421, 437, 438, 459, 461Google Scholar
Zemánek, J., A note on the radical of a Banach algebra. Manuscripta Math. 20 (1977), 191–6.Google Scholar
Zettl, H., A characterization of ternary rings of operators. Adv. Math. 48 (1983), 117–43. 459Google Scholar
Zhevlakov, K. A., Solvability of alternative nil-rings. Sibirsk. Mat. Z. 3 (1962), 368–77.Google Scholar
Zhevlakov, K. A., Coincidence of Smiley and Kleinfeld radicals in alternative rings. Algebra Logic 8 (1969), 175–81.Google Scholar
Zorn, M., Theorie der alternativen Ringe. Abh. Math. Sem. Univ. Hamburg 8 (1930), 123–47.Google Scholar
Zorn, M., Alternativkörper und quadratische Systeme. Abh. Math. Sem. Univ. Hamburg 9 (1933), 395402.Google Scholar
Albert, A. A., Structure of algebras. Revised printing, Amer. Math. Soc. Colloq. Publ. 24, American Mathematical Society, Providence, RI, 1961.Google Scholar
Albiac, F. and Kalton, N. J., Topics in Banach space theory . Grad. Texts in Math. 233, Springer, New York, 2006. 213, 236Google Scholar
Alfsen, E. M. and Shultz, F. W., Non-commutative spectral theory for affine function spaces on convex sets . Mem. Amer. Math. Soc. 6 (1976), no. 172.Google Scholar
Alfsen, E. M. and Shultz, F. W., Geometry of state spaces of operator algebras. Mathematics: Theory and Applications. Birkhäuser Boston, Inc., Boston, MA, 2003. 331, 411Google Scholar
Aliprantis, C. D. and Border, K. C., Infinite dimensional analysis. A hitchhiker’s guide. Third edition. Springer, Berlin, 2006.Google Scholar
Allan, G. R., Introduction to Banach spaces and algebras. Prepared for publication and with a preface by H. Garth Dales. Oxf. Grad. Texts Math. 20, Oxford University Press, Oxford, 2011.Google Scholar
Amir, D., Characterizations of inner product spaces. Oper. Theory Adv. Appl. 20, Birkhäuser Verlag, Basel–Boston–Stuttgart, 1986.Google Scholar
Andrunakievich, V. A. and Rjabuhin, Yu. M., Radicals of algebras and structural theory. (In Russian.) Contemporary Algebra ‘Nauka’, Moscow, 1979. 633 Google Scholar
Ara, P. and Mathieu, M., Local multipliers of C-algebras. Springer Monogr. Math., Springer, London, 2003. 401, 408, 550Google Scholar
Argyros, S. A. and Tolias, A., Methods in the theory of hereditarily indecomposable Banach spaces . Mem. Amer. Math. Soc. 170 (2004), no. 806.Google Scholar
Ash, R. B. and Novinger, W. P., Complex variables. Dover Publications, 2007.Google Scholar
Asimow, L. and Ellis, A. J., Convexity theory and its applications in functional analysis. London Math. Soc. Monogr. 16, Academic Press, London, 1980.Google Scholar
Aupetit, B., Propriétés spectrales des algèbres de Banach. Lecture Notes in Math. 735, Springer, Berlin, 1979. 401, 436, 498, 596, 597Google Scholar
Aupetit, B., A primer on spectral theory. Universitext, Springer, New York, 1991. 597, 599Google Scholar
Ayupov, S., Rakhimov, A., and Usmanov, S., Jordan, real and Lie structures in operator algebras . Math. Appl. 418, Kluwer Academic Publishers Group, Dordrecht, 1997.Google Scholar
Banach, S., Theory of linear operations. Translated from the French by F. Jellett. With comments by A. Pełczyński and Cz. Bessaga. North-Holland Math. Library 38, North-Holland Publishing Co., Amsterdam, 1987.Google Scholar
Beidar, K. I., Martindale, W. S. III, and Mikhalev, A. V., Rings with generalized identities . Monographs Textbooks Pure Appl. Math. 196, Marcel Dekker, New York, 1996. 401, 602Google Scholar
Beltita, D., Smooth homogeneous structures in operator theory. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 137, Chapman & Hall/CRC, Boca Raton, FL, 2006. xxiv, xxv, 154, 155, 174, 549, 554Google Scholar
Beltita, D. and Sabac, M., Lie algebras of bounded operators . Oper. Theory Adv. Appl. 120, Birkhäuser Verlag, Basel, 2001.Google Scholar
Berberian, S. K., Lectures in functional analysis and operator theory. Grad. Texts in Math. 15, Springer, New York–Heidelberg, 1974. 157, 183, 539Google Scholar
Blecher, D. P. and Merdy, Ch. Le, Operator algebras and their modules – an operator space approach. London Math. Soc. Monogr. New Series 30, Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford, 2004.Google Scholar
Block, R. E., Jacobson, N., Osborn, J. M., Saltman, D. J., and Zelinsky, D. (eds.), Adrian Albert, A., Collected mathematical papers: Associative algebras and Riemann matrices, Part 1. Amer. Math. Soc., Providence, RI, 1993. 664, 678Google Scholar
Block, R. E., Jacobson, N., Osborn, J. M., Saltman, D. J., and Zelinsky, D. (eds.), Adrian Albert, A., Collected mathematical papers: Nonassociative algebras and miscellany, Part 2. Amer. Math. Soc., Providence, RI, 1993. 664, 699Google Scholar
Boas, R. P., Entire functions. Academic Press Inc., New York, 1954.Google Scholar
Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras. London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, Cambridge, 1971.Google Scholar
Bonsall, F. F. and Duncan, J., Numerical ranges II. London Math. Soc. Lecture Note Ser. 10, Cambridge University Press, Cambridge, 1973.Google Scholar
Bonsall, F. F. and Duncan, J., Complete normed algebras. Ergeb. Math. Grenzgeb. 80, Springer, Berlin, 1973. xvii, 436, 545, 551, 584, 659Google Scholar
Bourbaki, N., Éléments de mathématique. Fasc. XXXII. Théories spectrales. Chapitre I: Algèbres normées. Chapitre II: Groupes localement compacts commutatifs . Actualités Scientifiques et Industrielles 1332, Hermann, Paris, 1967.Google Scholar
Bratteli, O., Derivations, dissipations and group actions on C-algebras . Lecture Notes in Math. 1229, Springer, Berlin, 1986.Google Scholar
Bratteli, O. and Robinson, D. W., Operator algebras and quantum statistical mechanics II . Texts Monographs Phys., Springer, New York, 1981.Google Scholar
Braun, H. and Koecher, M., Jordan-Algebren. Grundlehren Math. Wiss. 128, Springer, Berlin–New York, 1966.Google Scholar
Brelot, M., On topologies and boundaries in potential theory. (Enlarged edition of a course of lectures delivered in 1966). Lecture Notes in Math. 175, Springer, Berlin–New York, 1971.Google Scholar
Brešar, M., Chebotar, M. A., and Martindale, W. S. III, Functional identities. Front. Math., Birkhäuser Verlag, Basel, 2007. 602 Google Scholar
Caradus, S. R., Pfaffenberger, W. E., and Yood, B., Calkin algebras and algebras of operators on Banach spaces. Lecture Notes in Pure and Appl. Math. 9, Marcel Dekker Inc., New York, 1974.Google Scholar
Carmona, J., Morales, A., Peralta, A. M., and Ramírez, M. I. (eds.), Proceedings of Jordan structures in algebra and analysis meeting. Tribute to El Amin Kaidi for his 60th birthday. Almería 2009. Editorial Círculo Rojo, Almería 2010. 669, 674, 682Google Scholar
Castellón, A., Cuenca, J. A., Fernández, A., and Martín, C. (eds.), Proceedings of the International Conference on Jordan Structures (Málaga, 1997). Univ. Málaga, Málaga, 1999. 679, 680, 700, 707Google Scholar
Cerdà, J., Linear functional analysis. Grad. Stud. Math. 116, American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, 2010.Google Scholar
Chae, S. B., Holomorphy and calculus in normed spaces. With an appendix by Angus E. Taylor. Monographs Textbooks Pure Appl. Math. 92. Marcel Dekker Inc., New York, 1985. 23, 53Google Scholar
Chandid, A., Algèbres absolument valuées qui satisfont à (x p , x q , x r ) = 0. PhD thesis, Casablanca 2009.Google Scholar
Choquet, G., Cours d’analyse. Tome II: Topologie. Masson et Cie, Editeurs, Paris, 1964.Google Scholar
Chu, C.-H., Jordan structures in geometry and analysis. Cambridge Tracts in Math. 190, Cambridge University Press, New York, 2012. xix, 174, 207, 209, 210, 597, 711Google Scholar
Conway, J. B., A course in functional analysis. Second edition. Grad. Texts in Math. 96, Springer, New York, 1990.Google Scholar
Conway, J. H. and Smith, D. A., On quaternions and octonions: their geometry, arithmetic, and symmetry. A K Peters, Ltd., Natick, MA, 2003.Google Scholar
Cowie, E. R., Isometries in Banach algebras. PhD thesis, Swansea 1981.Google Scholar
Cuenca, J. A., Sobre H∗-álgebras no asociativas. Teoría de estructura de las H∗-álgebras de Jordan no conmutativas semisimples . PhD thesis, Granada 1982, Secretariado de Publicaciones de la Universidad de Málaga, 1984. xxiii, 545, 548, 597Google Scholar
Dales, H. G., Banach algebras and automatic continuity. London Math. Soc. Monogr. New Series 24, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 2000. 267, 414Google Scholar
Day, M. M., Normed linear spaces. Ergeb. Math. Grenzgeb. 21, Springer, Berlin, 1973.Google Scholar
Defant, A. and Floret, K., Tensor norms and operator ideals. North-Holland Math. Stud. 176, North-Holland Publishing Co., Amsterdam, 1993. 267, 356, 416, 646Google Scholar
Diestel, J., Geometry of Banach spaces – Selected topics, Lecture Notes in Math. 485, Springer, Berlin–Heidelberg–New York, 1975.Google Scholar
Diestel, J., Fourie, J. H., and Swart, J., The metric theory of tensor products . Grothendieck’s résumé revisited. American Mathematical Society, Providence, RI, 2008.Google Scholar
Diestel, J. and Uhl, J. J. Jr., Vector measures . Mathematical Surveys 15, American Mathematical Society, Providence, RI, 1977.Google Scholar
Dineen, S., The Schwarz lemma. Oxford Math. Monogr., Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1989. 79, 87, 88, 207, 211Google Scholar
Deville, R., Godefroy, G., and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs Surveys Pure Appl. Math. 64, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993.Google Scholar
Dixmier, J., Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann). Deuxième édition, revue et augmentée. Cahiers Scientifiques 25, Gauthier-Villars Éditeur, Paris, 1969. 492, 506Google Scholar
Dixmier, J., Les C∗-algèbres et leurs représentations. Deuxième édition. Cahiers Scientifiques 29, Gauthier-Villars Éditeur, Paris, 1969.Google Scholar
Doran, R. S. and Belfi, V. A., Characterizations of C∗-algebras: The Gelfand– Naimark theorems. Monographs Textbooks Pure Appl. Math. 101, Marcel Dekker, New York–Basel, 1986. xvii, 401Google Scholar
Dunford, N. and Schwartz, J. T., Linear operators. Part I. General theory. With the assistance of W. G. Bade and R. G. Bartle. Reprint of the 1958 original. Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1988. 12, 533, 541Google Scholar
Ebbinghaus, H.-D., Hermes, H., Hirzbruch, F., Koecher, H., Mainzer, K., Neukirch, J., Prestel, A., and Remmert, R., Numbers . Grad. Texts in Math. 123, Springer, New York, 1991. 409 Google Scholar
Elduque, A. and Myung, H. Ch., Mutations of alternative algebras . Math. Appl. 278, Kluwer Academic Publishers Group, Dordrecht, 1994.Google Scholar
Fabian, M., Habala, P., Hájek, P., Montesinos, V., and Zizler, V., Banach space theory. The basis for linear and nonlinear analysis . CMS Books Math., Springer, New York, 2011. 247, 249, 288, 338Google Scholar
Fleming, R. J. and Jamison, J. E., Isometries on Banach spaces. Vol. 1. Function spaces. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 129, Chapman & Hall/CRC, Boca Raton, FL, 2003.Google Scholar
Fleming, R. J. and Jamison, J. E., Isometries on Banach spaces. Vol. 2. Vector-valued function spaces. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 138, Chapman & Hall/CRC, Boca Raton, FL, 2008.Google Scholar
Friedmann, Y. and Scarr, T., Physical applications of homogeneous balls. Prog. Math. Phys. 40, Birhäuser, Boston, 2005. 207 Google Scholar
González, S. (ed.), Nonassociative algebra and its applications (Oviedo, 1993). Math. Appl. 303, Kluwer Academic Publishers, Dordrecht–Boston–London 1994. 679, 681, 685, 690, 702, 706Google Scholar
González, S. and Myung, H. Ch. (eds.), Nonassociative algebraic models. Proceedings of the workshop held at the Universidad de Zaragoza, Zaragoza, April 1989 . Nova Science Publishers, Inc., Commack, NY, 1992. 671, 675, 685, 701, 702, 709Google Scholar
Goodearl, K. R., Notes on real and complex C-algebras. Shiva Mathematics Series 5. Shiva Publishing Ltd., Nantwich, 1982.Google Scholar
Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. (1955), no. 16.Google Scholar
Hamilton, W. R., On quaternions, or on a new system of imaginaries in Algebra. Philosophical Magazine, (1844–1850), ed. D. R. Wilkins, 2000. http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/OnQuat/OnQuat.pdf Google Scholar
Hanche-Olsen, H. and Størmer, E., Jordan operator algebras . Monographs and Studies in Mathematics 21, Pitman, Boston, 1984. xviii, xx, xxi, 3, 8, 9, 11, 12, 13, 14, 286, 330, 332, 339, 347, 348, 362, 398, 399, 401, 416, 551Google Scholar
Harmand, P., Werner, D., and Werner, W., M-ideals in Banach spaces and Banach algebras. Lecture Notes in Math. 1547, Springer, Berlin, 1993. 19, 266, 267Google Scholar
de la Harpe, P., Classical Banach–Lie algebras and Banach–Lie groups of operators in Hilbert space. Lecture Notes in Math. 285, Springer, Berlin–New York, 1972. 554 Google Scholar
Hazewinkel, M. (ed.), Encyclopaedia of mathematics, suplement III. Kluwer Academic Publishers, 2002. 679, 685, 703Google Scholar
Helemskii, A. Ya., Banach and locally convex algebras. Translated from Russian by A. West. Oxford Sci. Publ., The Clarendon Press, Oxford University Press, New York, 1993.Google Scholar
Herstein, I. N., Topics in ring theory. The University of Chicago Press, Chicago, 1969. 367, 510Google Scholar
Herstein, I. N., Noncommutative rings. Reprint of the 1968 original. With an afterword by Lance W. Small. Carus Mathematical Monographs 15, Mathematical Association of America, Washington, DC, 1994.Google Scholar
Hille, E., Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, New York, 1948.Google Scholar
Hille, E. and Phillips, R. S., Functional analysis and semi-groups. Third printing of the revised edition of 1957. Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, Providence, RI, 1974.Google Scholar
Hoffman, K., Banach spaces of analytic functions. Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1962.Google Scholar
Iochum, B., Cônes autopolaires et algèbres de Jordan . Lecture Notes in Math. 1049, Springer, Berlin, 1984.Google Scholar
Iochum, B. and Loupias, G. (eds.), Colloque sur les algèbres de Jordan, Montpellier, Octobre 1985 . Ann. Sci. Univ. ‘Blaise Pascal’, Clermont II, Sér. Math . 27 (1991). 674, 679, 681, 685, 702Google Scholar
Iordanescu, R., Jordan structures in analysis, geometry and physics. Editura Academiei Române, Bucharest, 2009. 597 Google Scholar
Isidro, J. M. and Stachó, L. L., Holomorphic automorphism groups in Banach spaces: an elementary introduction . North-Holland Math. Stud. 105, North-Holland Publishing Co., Amsterdam, 1985. xix, 53, 87, 88, 135, 174, 207, 211Google Scholar
Jacobson, N., Lie algebras. Interscience Tracts in Pure and Applied Mathematics 10, Interscience Publishers, New York–London, 1962. 549 Google Scholar
Jacobson, N., Structure of rings. Amer. Math. Soc. Colloq. Publ. 37, Providence, RI, 1964. 500, 559, 598Google Scholar
Jacobson, N., Structure and representations of Jordan algebras . Amer. Math. Soc. Colloq. Publ. 39, Providence, RI, 1968. 472, 594, 597Google Scholar
Jacobson, N., Structure theory of Jordan algebras . University of Arkansas Lecture Notes in Mathematics 5, University of Arkansas, Fayetteville, AR, 1981. 361 Google Scholar
Jameson, G. J. O., Topology and normed spaces. Chapman and Hall, London; Halsted Press [John Wiley & Sons], New York, 1974.Google Scholar
Johnson, W. B. and Lindenstrauss, J. (eds.), Handbook of the geometry of Banach spaces. Vol. 2. North-Holland, Amsterdam, 2003. 671, 681Google Scholar
Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vol. I. Elementary theory . Grad. Stud. Math. 15, American Mathematical Society, Providence, RI, 1997. 330, 366, 459Google Scholar
Kaidi, A., Bases para una teoría de las álgebras no asociativas normadas . PhD thesis, Granada 1978. 597 Google Scholar
Kantor, I. L. and Solodovnikov, A. S., Hypercomplex numbers. An elementary introduction to algebras. Translated from Russian by A. Shenitzer. Springer, New York, 1989.Google Scholar
Kaplansky, I., Rings of operators. Math. Lecture Note Ser., W. A. Benjamin, Inc., New York–Amsterdam, 1968. xxi, 398Google Scholar
Kaplansky, I., Algebraic and analytic aspects of operator algebras. CBMS Regional Conf. Ser. in Math. 1, American Mathematical Society, Providence, RI, 1970.Google Scholar
Kargapolov, M. I. and Merzljakov, Ju. I., Fundamentals of the theory of groups. Translated from the second Russian edition by Robert G. Burns. Grad. Texts in Math. 62, Springer-Verlag, New York–Berlin, 1979. 633 Google Scholar
Kaup, W., McCrimmon, K., and Petersson, H. P. (eds.), Jordan algebras, Proceedings of the conference held in Oberwolfach, Germany, August 9–15, 1992. Walter de Gruyter, Berlin–New York, 1994. 685, 686Google Scholar
Knus, M.-A., Merkurjev, A., Rost, M., and Tignol, J.-P., The book of involutions. Amer. Math. Soc. Colloq. Publ. 44, Providence, RI, 1998.Google Scholar
Lam, T. Y., A first course in noncommutative rings. Second edition. Grad. Texts in Math. 131, Springer, New York, 2001.Google Scholar
Laursen, K. B. and Neumann, M. M., An introduction to local spectral theory. London Math. Soc. Monogr. New Series 20, Clarendon Press, Oxford, 2000. 596 Google Scholar
Li, B., Real operator algebras. World Scientific Publishing Co., Inc., River Edge, NJ, 2003. 549 Google Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. I. Sequence spaces. Ergeb. Math. Grenzgeb. 92, Springer, Berlin–New York, 1977. 261 Google Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. II. Function spaces. Ergeb. Math. Grenzgeb. 97, Springer, Berlin–New York, 1979.Google Scholar
Loos, O., Jordan pairs. Lecture Notes in Math. 460, Springer, Berlin–New York, 1975. 445 Google Scholar
Loos, O., Bounded symmetric domains and Jordan pairs. Lecture Notes, University of California, Irvine, 1977. 211, 337, 441, 444, 454, 460Google Scholar
Loy, R. J. (ed.), Conference on Automatic Continuity and Banach Algebras (Canberra, 1989). Proc. Centre Math. Anal. Austral. Nat. Univ. 21, Austral. Nat. Univ., Canberra, 1989. 672, 681Google Scholar
Martín, M., Índice numérico de un espacio de Banach . PhD thesis, Granada 2000.Google Scholar
Martínez, J., Sobre álgebras de Jordan normadas completas . PhD thesis, Granada 1977. Tesis Doctorales de la Universidad de Granada 149, Secretariado de Publicaciones de la Universidad de Granada, 1977. 597Google Scholar
Mauldin, R. D. (ed.), The Scottish book. Mathematics from the Scottish café. Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. Birkhäuser, Boston, Mass., 1981.Google Scholar
McCrimmon, K., A taste of Jordan algebras . Universitext, Springer, New York, 2004 361, 364, 401, 589, 591, 598Google Scholar
Megginson, R. E., An introduction to Banach space theory. Grad. Texts in Math. 183, Springer, New York, 1998. 7, 220, 340Google Scholar
Meyberg, A., Lectures on algebras and triple systems. Lecture notes, The University of Virginia, Charlottesville, 1972.Google Scholar
Müller, V., Spectral theory of linear operators and spectral systems in Banach algebras. Second edition. Oper. Theory Adv. Appl. 139, Birkhäuser Verlag, Basel, 2007.Google Scholar
Murphy, G. J., C-algebras and operator theory. Academic Press, Inc., Boston, MA, 1990. 330, 408Google Scholar
Myung, H. Ch., Malcev-admissible algebras . Progr. Math. 64, Birkhäuser Boston, Inc., Boston, MA, 1986.Google Scholar
Naimark, M. A., Normed algebras. Translated from the second Russian edition by Leo F. Boron. Third edition. Wolters–Noordhoff Series of Monographs and Textbooks on Pure and Applied Mathematics, Wolters–Noordhoff Publishing, Groningen, 1972. 551 Google Scholar
Ocaña, F. G., El axioma de Sakai en JV-álgebras. PhD thesis, Granada 1979. Tesis Doctorales de la Universidad de Granada 224, Secretariado de Publicaciones de la Universidad de Granada, 1979.Google Scholar
Okubo, S., Introduction to octonion and other non-associative algebras in physics. Montroll Memorial Lecture Ser. Math. Phys. 2, Cambridge University Press, Cambridge, 1995.Google Scholar
Palmer, T. W., Banach algebras and the general theory of ∗-algebras, Volume I, algebras and Banach algebras. Encyclopedia Math. Appl. 49, Cambridge University Press, Cambridge, 1994. xxvi, 650, 651, 652, 654Google Scholar
Palmer, T. W., Banach algebras and the general theory of ∗-algebras, Volume II, ∗-algebras. Encyclopedia Math. Appl. 79, Cambridge University Press, Cambridge, 2001. xvii Google Scholar
Paulsen, V., Completely bounded maps and operator algebras. Cambridge Stud. Adv. Math. 78, Cambridge University Press, Cambridge, 2002. 273 Google Scholar
Pedersen, G., Analysis now. Grad. Texts in Math. 118, Springer, New York, 1989. 330 Google Scholar
Pietsch, A., History of Banach spaces and linear operators. Birkhäuser Boston, Inc., Boston, MA, 2007. 236, 550Google Scholar
Pisier, G., Introduction to operator space theory. London Math. Soc. Lecture Note Ser. 294, Cambridge University Press, Cambridge, 2003.Google Scholar
Przeworska-Rolewicz, D., Linear spaces and linear operators. Institute of Mathematics of the Polish Academy of Sciences, Warsaw, 2007.Google Scholar
Ransford, T., Potential theory in the complex plane. London Math. Soc. Stud. Texts 28, Cambridge University Press, Cambridge, 1995.Google Scholar
Razmyslov, Yu. P., Identities of algebras and their representations. Transl. Math. Monogr. 138, American Mathematical Society, Providence, RI, 1994.Google Scholar
Rickart, C. E., General theory of Banach algebras. The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, NJ–Toronto–London–New York, 1960. 335, 481, 524, 548, 551Google Scholar
Riesz, F. and Sz-Nagy, B., Leçons d’analyse fonctionelle. Cinquième édition. Gauthier-Villars, Paris; Akadémiai Kiadó, Budapest, 1968. 330 Google Scholar
Roch, S., Santos, P. A., and Silbermann, B., Non-commutative Gelfand theories. A tool-kit for operator theorists and numerical analysts . Universitext, Springer London, Ltd., London, 2011.Google Scholar
Rodríguez, A., Contribución a la teoría de las C-álgebras con unidad . PhD thesis, Granada 1974. Tesis Doctorales de la Universidad de Granada 57, Secretariado de Publicaciones de la Universidad de Granada, 1974. 336 Google Scholar
Rodríguez, A., Números hipercomplejos en dimensión infinita . Discurso de ingreso en la Academia de Ciencias Matemáticas, Físico-Químicas y Naturales de Granada, Granada, 1993. 409 Google Scholar
Rolewicz, S., Metric linear spaces. Math. Appl. 20, D. Reidel Publishing Co., Dordrecht; PWN-Polish Scientific Publishers, Warsaw, 1985. 196 Google Scholar
Rose, H. E., Linear algebra. A pure mathematical approach. Birkhäuser Verlag, Basel, 2002.Google Scholar
Rowen, L. H., Ring theory, Volume I . Pure Appl. Math. 127. Academic Press, Inc., Boston, 1988.Google Scholar
Rudin, W., Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. 425, 433Google Scholar
Rudin, W., Functional analysis. Second edition. Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc., New York, 1991.Google Scholar
Rynne, B. P. and Youngson, M. A., Linear functional analysis . Second edition. Springer Undergrad. Math. Ser., Springer London, Ltd., London, 2008.Google Scholar
Sakai, S., C-algebras and W-algebras. Ergeb. Math. Grenzgeb. 60, Springer, New York–Heidelberg, 1971. 19, 329, 331, 339, 399, 421Google Scholar
Sakai, S., Operator algebras in dynamical systems. The theory of unbounded derivations in C-algebras. Encyclopedia Math. Appl. 41, Cambridge University Press, Cambridge, 1991.Google Scholar
Schafer, R. D., An introduction to nonassociative algebras. Corrected reprint of the 1966 original. Dover Publications, Inc., New York, 1995. 208, 360, 361, 401, 545, 652Google Scholar
Schatten, R., Norm ideals of completely continuous operators . Second printing. Ergeb. Math. Grenzgeb. 27, Springer, Berlin–New York, 1970. 409, 481, 494, 524, 531, 532, 533Google Scholar
Sinclair, A. M., Automatic continuity of linear operators. London Math. Soc. Lecture Note Ser. 21, Cambridge University Press, Cambridge–New York–Melbourne, 1976. 499 Google Scholar
Taylor, A. E. and Lay, D. C., Introduction to Functional Analysis. Second edition. John Wiley & Sons, New York–Chichester–Brisbane, 1980.Google Scholar
Tian, J. P., Evolution algebras and their applications. Lecture Notes in Math. 1921, Springer, Berlin, 2008.Google Scholar
Topping, D. M., Jordan algebras of self-adjoint operators. Mem. Amer. Math. Soc. (1965), no. 53. 400Google Scholar
Upmeier, H., Symmetric Banach Manifolds and Jordan C-algebras. North-Holland Math. Stud. 104, North-Holland, Amsterdam, 1985. xix, 52, 53, 87, 135, 174, 207, 211, 597Google Scholar
Upmeier, H. Jordan algebras in analysis, operator theory, and quantum mechanics. CBMS Regional Conf. Ser. in Math. 67, American Mathematical Society, Providence, RI, 1987. 1987. 53, 87, 135, 174, 207, 211Google Scholar
Villena, A. R., Algunas cuestiones sobre las JB∗-álgebras: centroide, centroide extendido y zócalo . PhD thesis, Granada 1990.Google Scholar
Wilansky, A., Modern methods in topological vector spaces. McGraw-Hill International Book Co., New York, 1978.Google Scholar
Wilansky, A., Topology for analysis. Reprint of the 1970 edition. Robert E. Krieger Publishing Co., Inc., Melbourne, FL, 1983.Google Scholar
Wisbauer, R., Modules and algebras: bimodule structure and group actions on algebras. Pitman Monographs Surveys Pure Appl. Math. 81, Longman, Harlow, 1996.Google Scholar
Zelazko, W., Banach algebras. Translated from Polish by Marcin E. Kuczma. Elsevier Publishing Co., Amsterdam–London–New York; PWN-Polish Scientific Publishers, Warsaw, 1973.Google Scholar
Zemánek, J., Properties of the spectral radius in Banach algebras. PhD thesis, Warszawa 1977.Google Scholar
Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P., and Shirshov, A. I., Rings that are nearly associative. Translated from Russian by Harry F. Smith. Pure Appl. Math. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York–London, 1982. 360, 361, 401, 413, 414, 415, 570, 571, 597, 631, 636, 647Google Scholar

Secondary Sources

Acosta, M. D., Becerra, J., and Rodríguez, A., Weakly open sets in the unit ball of the projective tensor product of Banach spaces. J. Math. Anal. Appl. 383 (2011), 461–73.Google Scholar
Adams, J. F., On the structure and applications of the Steenrod algebra. Comment. Math. Helv. 32 (1958), 180214.CrossRefGoogle Scholar
Akemann, C. A. and Pedersen, G. K., Complications of semicontinuity in C -algebra theory. Duke Math. J. 40 (1973), 785–95. 346Google Scholar
Akemann, C. A. and Pedersen, G. K., Facial structure in operator algebra theory. Proc. London Math. Soc. 64 (1992), 418–48.Google Scholar
Akemann, C. A. and Weaver, N., Geometric characterizations of some classes of operators in C -algebras and von Neumann algebras. Proc. Amer. Math. Soc. 130 (2002), 3033–7.Google Scholar
Albert, A. A., On a certain algebra of quantum mechanics. Ann. of Math. 35 (1934), 6573. Reprinted in [692], pp. 85–93.CrossRefGoogle Scholar
Albert, A. A., Quadratic forms permitting composition. Ann. of Math. 43 (1942), 161–77. Reprinted in [692], pp. 219–35.Google Scholar
Albert, A. A., The radical of a non-associative algebra. Bull. Amer. Math. Soc. 48 (1942), 891–7. Reprinted in [692], pp. 277–83. 546Google Scholar
Albert, A. A., Absolute valued real algebras. Ann. of Math. 48 (1947), 495501. Reprinted in [691], pp. 643–9.Google Scholar
Albert, A. A., A structure theory for Jordan algebras. Ann. of Math. 48 (1947), 546–67. Reprinted in [692], pp. 401–22.Google Scholar
Albert, A. A., On the power-associativity of rings. Summa Brasil. Math. 2 (1948), 2132. Reprinted in [692], pp. 423–35.Google Scholar
Albert, A. A., Power-associative rings. Trans. Amer. Math. Soc. 608 (1948), 552–93. Reprinted in [692], pp. 437–78. 273Google Scholar
Albert, A. A., Absolute valued algebraic algebras. Bull. Amer. Math. Soc. 55 (1949), 763–8. Reprinted in [691], pp. 651–6.Google Scholar
Albert, A. A., A note of correction. Bull. Amer. Math. Soc. 55 (1949), 1191.Google Scholar
Alfsen, E. M., Shultz, F. W., and Størmer, E., Gelfand, ANeumark theorem for Jordan algebras. Adv. Math. 28 (1978), 1156. 398, 401Google Scholar
Allan, G. R., Some simple proofs in holomorphic spectral theory. In Perspectives in operator theory, pp. 915, Banach Center Publ. 75, Polish Acad. Sci. Inst. Math., Warsaw, 2007.Google Scholar
Alvermann, K., The multiplicative triangle inequality in noncommutative JB- and JB -algebras. Abh. Math. Sem. Univ. Hamburg 55 (1985), 91–6.Google Scholar
Alvermann, K., Real normed Jordan Banach algebras with an involution. Arch. Math. (Basel) 47 (1986), 135–50.CrossRefGoogle Scholar
Alvermann, K. and Janssen, G., Real and complex non-commutative Jordan Banach algebras. Math. Z. 185 (1984), 105–13. xix, xx, 19, 267, 268, 334, 335, 398, 411, 421Google Scholar
Ambrose, W., Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364886. xxiii, xxv, 477, 545, 550Google Scholar
Anquela, J. A., Montaner, F., and Cortés, T., On primitive Jordan algebras. J. Algebra 163 (1994), 663–74. xxii, 462, 466CrossRefGoogle Scholar
Aparicio, C., Ocaña, F. G., Payá, R., and Rodríguez, A., A non-smooth extension of Fréchet differentiability of the norm with applications to numerical ranges. Glasgow Math. J. 28 (1986), 121–37.Google Scholar
Aparicio, C. and Rodríguez, A., Sobre el espectro de derivaciones y automorfismos de las álgebras de Banach. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 79 (1985), 113–18.Google Scholar
Araki, H. and Elliott, G. A., On the definition of C -algebras. Publ. Res. Inst. Math. Sci. 9 (1973/74), 93112.Google Scholar
Arazy, J., Isometries of Banach algebras satisfying the von Neumann inequality. Math. Scand. 74 (1994), 137–51. 136, 207Google Scholar
Arazy, J. and Solel, B., Isometries of nonselfadjoint operator algebras. J. Funct. Anal. 90 (1990), 284305. 207CrossRefGoogle Scholar
Arendt, W., Chernoff, P. R., and Kato, T., A generalization of dissipativity and positive semigroups. J. Operator Theory 8 (1982), 167–80.Google Scholar
Arens, R., Operations induced in function classes. Monatsh. Math. 55 (1951), 119.CrossRefGoogle Scholar
Arens, R., The adjoint of a bilinear operation. Proc. Amer. Math. Soc. 2 (1951), 839–48.Google Scholar
Arens, R. and Kaplansky, I., Topological representation of algebras. Trans. Amer. Math. Soc. 63 (1948), 457–81.Google Scholar
Argyros, S. A. and Felouzis, V., Interpolating hereditarily indecomposable Banach spaces. J. Amer. Math. Soc. 13 (2000), 243–94.CrossRefGoogle Scholar
Argyros, S. A. and Haydon, R. G., A hereditarily indecomposable L -space that solves the scalar-plus-compact problem. Acta Math. 206 (2011), 154.Google Scholar
Argyros, S. A., López-Abad, J., and Todorcevic, S., A class of Banach spaces with few non-strictly singular operators. J. Funct. Anal. 222 (2005), 306–84.Google Scholar
Aron, R. M. and Lohman, R. H., A geometric function determined by extreme points of the unit ball of a normed space. Pacific J. Math. 127 (1987), 209–31.Google Scholar
Arosio, A., Locally convex inductive limits of normed algebras. Rend. Sem. Mat. Univ. Padova 51 (1974), 333–59.Google Scholar
Auerbach, H., Sur les groupes linéaires I, II, III. Studia Math . 4 (1934), 113–27; Ibid. 4 (1934), 158–66; Ibid. 5 (1935), 43–9.Google Scholar
Aupetit, B., Symmetric almost commutative Banach algebras. Notices Amer. Math. Soc. 18 (1971), 559–60.Google Scholar
Aupetit, B., Caractérisation spectrale des algèbres de Banach commutatives. Pacific J. Math. 63 (1976), 2335.CrossRefGoogle Scholar
Aupetit, B., Caractérisation spectrale des algèbres de Banach de dimension finie. J. Funct. Anal. 26 (1977), 232–50.Google Scholar
Aupetit, B., The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras. J. Funct. Anal. 47 (1982), 16. x, 597Google Scholar
Aupetit, B., Recent trends in the field of Jordan–Banach algebras. In [1189], pp. 9–19. 597Google Scholar
Aupetit, B., Analytic Multifunctions and their applications. In Complex potential theory (ed. Gauthier, P. M.), pp. 174, Kluwer Academic Publishers, Dordrecht– Boston–London 1994.Google Scholar
Aupetit, B., Spectral characterization of the socle in Jordan–Banach algebras. Math. Proc. Cambridge Philos. Soc. 117 (1995), 479–89. 601CrossRefGoogle Scholar
Aupetit, B., Trace and spectrum preserving linear mappings in Jordan–Banach algebras. Monatsh. Math. 125 (1998), 179–87. 601Google Scholar
Aupetit, B. and Baribeau, L., Sur le socle dans les algèbres de Jordan–Banach. Canad. J. Math. 41 (1989), 1090–100. 599Google Scholar
Aupetit, B. and Maouche, A., Trace and determinant in Jordan–Banach algebras. Publ. Mat. 46 (2002), 316. 601Google Scholar
Aupetit, B. and Mathieu, M., The continuity of Lie homomorphisms. Studia Math. 138 (2000), 193–99. 603Google Scholar
Aupetit, B. and Youngson, M. A., On symmetry of Banach Jordan algebras. Proc. Amer. Math. Soc. 91 (1984), 364–6. 597Google Scholar
Avilés, A. and Koszmider, P., A Banach space in which every injective operator is surjective. Bull. London Math. Soc. 45 (2013), 1065–74.Google Scholar
Baer, R., Radical ideals. Amer. J. Math. 65 (1943), 537–68.Google Scholar
Baez, J. C., The octonions. Bull. Amer. Math. Soc. 39 (2002), 145205. Errata. Ibid. 42 (2005), 213.Google Scholar
Baillet, M., Analyse spectrale des opérateurs hermitiens d’une espace de Banach. J. London Math. Soc. 19 (1979), 497508.Google Scholar
Balachandran, V. K., Simple L -algebras of classical type. Math. Ann. 180 (1969), 205–19. 554Google Scholar
Balachandran, V. K. and Rema, P. S., Uniqueness of the norm topology in certain Banach Jordan algebras. Publ. Ramanujan Inst. 1 (1969), 283–9. 597Google Scholar
Balachandran, V. K. and Swaminatan, N., Real H -algebras. J. Funct. Anal. 65 (1986), 6475. 551CrossRefGoogle Scholar
Bandyopadhyay, P., Jarosz, K., and Rao, T. S. S. R. K., Unitaries in Banach spaces. Illinois J. Math. 48 (2004), 339–51.Google Scholar
Barnes, B. A., Locally B -equivalent algebras. Trans. Amer. Math. Soc. 167 (1972), 435–42.Google Scholar
Barnes, B. A., Locally B -equivalent algebras II. Trans. Amer. Math. Soc. 176 (1973), 297303.Google Scholar
Barnes, B. A., A note on invariance of spectrum for symmetric Banach ∗-algebras. Proc. Amer. Math. Soc. 126 (1998), 3545–7.Google Scholar
Barton, T. J. and Friedman, Y., Bounded derivations of JB -triples. Quart. J. Math. Oxford 41 (1990), 255–68. xx, 274, 337, 338Google Scholar
Bauer, F. L., On the field of values subordinate to a norm. Numer. Math. 4 (1962), 103–11.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Banach algebras with large groups of unitary elements. Quart. J. Math. Oxford 58 (2007), 203–20.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Banach spaces whose algebras of operators have a large group of unitary elements. Math. Proc. Camb. Phil. Soc. 144 (2008), 97108.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Nonassociative unitary Banach algebras. J. Algebra 320 (2008), 3383–97.Google Scholar
Becerra, J., Cowell, S., Rodríguez, A., and Wood, G. V., Unitary Banach algebras. Studia Math. 162 (2004), 2551.Google Scholar
Becerra, J., López, G., Peralta, A. M., and Rodríguez, A., Relatively weakly open sets in closed balls of Banach spaces, and real JB -triples of finite rank. Math. Ann. 330 (2004), 4558. 243, 274, 336Google Scholar
Becerra, J., López, G., and Rodríguez, A., Relatively weakly open sets in closed balls of C -algebras. J. London Math. Soc. 68 (2003), 753–61. 274, 336, 421Google Scholar
Becerra, J., Moreno, A., and Rodríguez, A., Absolute-valuable Banach spaces. Illinois J. Math. 49 (2005), 121–38.Google Scholar
Becerra, J. and Peralta, A. M., Subdifferentiability of the norm and the Banach–Stone theorem for real and complex JB -triples. Manuscripta Math. 114 (2004), 503–16.Google Scholar
Becerra, J. and Rodríguez, A., Isometric reflections on Banach spaces after a paper of A. Skorik and M. Zaidenberg. Rocky Mountain J. Math. 30 (2000), 6383.Google Scholar
Becerra, J. and Rodríguez, A., Transitivity of the norm on Banach spaces having a Jordan structure, Manuscripta Math. 102 (2000), 111–27. 210Google Scholar
Becerra, J. and Rodríguez, A., Characterizations of almost transitive superrreflexive Banach spaces. Comment. Math. Univ. Carolinae 42 (2001), 629–36.Google Scholar
Becerra, J. and Rodríguez, A., Transitivity of the norm on Banach spaces. Extracta Math. 17 (2002), 158.Google Scholar
Becerra, J. and Rodríguez, A., Strong subdifferentiability of the norm on JB -triples. Quart. J. Math. Oxford 54 (2003), 381–90.Google Scholar
Becerra, J. and Rodríguez, A., Big points in C -algebras and JB -triples. Quart. J. Math. Oxford 56 (2005), 141–64.Google Scholar
Becerra, J. and Rodríguez, A., Absolute-valued algebras with involution, and infinite-dimensional Terekhin’s trigonometric algebras. J. Algebra 293 (2005), 448–56.Google Scholar
Becerra, J. and Rodríguez, A., Non self-adjoint idempotents in C - and JB -algebras. Manuscripta Math. 124 (2007), 183–93.Google Scholar
Becerra, J. and Rodríguez, A., C - and JB -algebras generated by a non-self-adjoint idempotent. J. Funct. Anal. 248 (2007), 107–27.Google Scholar
Becerra, J. and Rodríguez, A., Locally uniformly rotund points in convex-transitive Banach spaces. J. Math. Anal. Appl. 360 (2009), 108–18.Google Scholar
Becerra, J., Rodríguez, A., and Wood, G. V., Banach spaces whose algebras of operators are unitary: a holomorphic approach. Bull. London Math. Soc. 35 (2003), 218–24. 210Google Scholar
Beddaa, A. and Oudadess, M., On a question of A. Wilansky in normed algebras. Studia Math. 95 (1989), 175–7.Google Scholar
Behncke, H., Hermitian Jordan Banach algebras. J. London Math. Soc. 20 (1979), 327–33. 597Google Scholar
Behncke, H. and Nyamwala, F. O., Two projections and one idempotent. Int. J. Pure Appl. Math. 52 (2009), 501–10.Google Scholar
Bell, J. P. and Small, L. W., A question of Kaplansky. J. Algebra 258 (2002), 386–8.Google Scholar
Bensebah, A., JV-algèbres et JH -algèbres. Canad. Math. Bull. 34 (1991), 447–55. 549, 597Google Scholar
Bensebah, A., Weakness of the topology of a JB -algebra. Canad. Math. Bull. 35 (1992), 449–54. 597Google Scholar
Benslimane, M. and Boudi, N., Alternative Noetherian Banach Algebras. Extracta Math. 12 (1997), 41–6. 601Google Scholar
Benslimane, M. and Boudi, N., Noetherian Jordan Banach algebras are finite-dimensional. J. Algebra 213 (1999), 340–50. 601Google Scholar
Benslimane, M., Fernández, A., and Kaidi, A., Caractérisation des algèbres de Jordan– Banach de capacité finie. Bull. Sci. Math. 112 (1988), 473–80. 597, 598, 599Google Scholar
Benslimane, M., Jaa, O., and Kaidi, A., The socle and the largest spectrum finite ideal. Quart. J. Math. Oxford 42 (1991), 17. 599, 601Google Scholar
Benslimane, M. and Kaidi, A., Structure des algèbres de Jordan–Banach non commutatives complexes régulières ou semi-simples à spectre fini. J. Algebra 113 (1988), 201–6. xxv, 596, 597, 598CrossRefGoogle Scholar
Benslimane, M. and Merrachi, N., Algèbres de Jordan Banach vérifiant ‖x‖‖x −1‖ = 1. J. Algebra 206 (1998), 129–34.Google Scholar
Benslimane, M. and Merrachi, N., Algèbres à puissances associatives normées sans J-diviseurs de zéro. Algebras Groups Geom. 16 (1999), 355–61.Google Scholar
Benslimane, M. and Moutassim, A., Some new class of absolute-valued algebras with left-unit. Adv. Appl. Clifford Algebras 21 (2011), 3140.Google Scholar
Benslimane, M. and Rodríguez, A., Caractérisation spectrale des algèbres de Jordan Banach non commutatives complexes modulaires annihilatrices. J. Algebra 140 (1991), 344–54. 599Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie derivations on Banach algebras. Proc. Edinburgh Math. Soc. 41 (1998), 625–30.Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie mappings of the skew elements of Banach algebras with involution. Proc. Amer. Math. Soc. 126 (1998), 2717–20.Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie isomorphisms of Banach algebras. Bull. London Math. Soc. 31 (1999), 610.Google Scholar
Berenguer, M. I. and Villena, A. R., On the range of a Lie derivation on a Banach algebra. Comm. Algebra 28 (2000), 1045–50.Google Scholar
Berkson, E., Some characterizations of C -algebras. Illinois J. Math. 10 (1966), 18.Google Scholar
Beurling, A., Sur les intégrales de Fourier absolument convergentes et leur application à fonctionelle. In Neuvième congrès des mathématiciens scandinaves. Helsingfors, 1938, pp. 345–66.Google Scholar
Biss, D. K., Christensen, J. D., Dugger, D., and Isaksen, D. C., Large annihilators in Cayley–Dickson algebras II. Bol. Soc. Mat. Mexicana 13 (2007), 269–92.Google Scholar
Biss, D. K., Christensen, J. D., Dugger, D., and Isaksen, D. C., Eigentheory of Cayley– Dickson algebras. Forum Math. 21 (2009), 833–51.Google Scholar
Biss, D. K., Dugger, D., and Isaksen, D. C., Large annihilators in Cayley–Dickson algebras. Comm. Algebra 36 (2008), 632–64.Google Scholar
Blecher, D. and Magajna, B., Dual operator systems. Bull. London Math. Soc. 43 (2011), 311–20.Google Scholar
Blecher, D. P., Ruan, Z.-J., and Sinclair, A. M., A characterization of operator algebras. J. Funct. Anal. 89 (1990), 188201.Google Scholar
Boas, R. P., Entire functions of exponential type. Bull. Amer. Math. Soc. 48 (1942), 839–49.Google Scholar
Bohnenblust, H. F. and Karlin, S., Geometrical properties of the unit sphere of a Banach algebra. Ann. of Math. 62 (1955), 217–29.Google Scholar
Bollobás, B., An extension to the theorem of Bishop and Phelps. Bull. London Math. Soc. 2 (1970), 181–2.Google Scholar
Bollobás, B., The numerical range in Banach algebras and complex functions of exponential type. Bull. London Math. Soc. 3 (1971), 2733.Google Scholar
Bonsall, F. F., A minimal property of the norm in some Banach algebras. J. London Math. Soc. 29 (1954), 156–64.Google Scholar
Bonsall, F. F., Locally multiplicative wedges in Banach algebras. Proc. London Math. Soc. 30 (1975), 239–56.Google Scholar
Bonsall, F. F., Jordan algebras spanned by Hermitian elements of a Banach algebra. Math. Proc. Cambridge Philos. Soc. 81 (1977), no. 1, 313.Google Scholar
Bonsall, F. F., Jordan subalgebras of Banach algebras. Proc. Edinburgh Math. Soc. 21 (1978), 103–10.Google Scholar
Bonsall, F. F. and Crabb, M. J., The spectral radius of a Hermitian element of a Banach algebra. Bull. London Math. Soc. 2 (1970), 178–80.Google Scholar
Bonsall, F. F. and Duncan, J., Dually irreducible representations of Banach algebras, Quart. J. Math. Oxford 19 (1968), 97111.Google Scholar
Bott, R. and Milnor, J., On the parallelizability of the spheres. Bull. Amer. Math. Soc. 64 (1958), 87–9.Google Scholar
Böttcher, A. and Spitkovsky, I. M., A gentle guide to the basics of two projections theory. Linear Algebra Appl. 432 (2010), 1412–59.CrossRefGoogle Scholar
Boudi, N., On Jordan Banach algebras with countably generated inner ideals. Algebra Colloq. 17 (2010), 211–22. 601Google Scholar
Boudi, N., Marhnine, H., Zarhouti, C., Fernández, A., and García, E., Noetherian Banach Jordan pairs. Math. Proc. Cambridge Philos. Soc. 130 (2001), 2536. 601Google Scholar
Bouhya, K. and Fernández, A., Jordan-∗-triples with minimal inner ideals and compact JB -triples. Proc. London Math. Soc. 68 (1994), 380–98. 241, 461, 603Google Scholar
Boyko, K., Kadets, V., Martín, M., and Werner, D., Numerical index of Banach spaces and duality. Math. Proc. Cambridge Philos. Soc. 142 (2007), 93102.Google Scholar
Bratteli, O. and Robinson, D. W., Unbounded derivations of C -algebras. II. Comm. Math. Phys. 46 (1976), 1130.Google Scholar
Braun, R. B., Structure and representations of non-commutative C -Jordan algebras. Manuscripta Math. 41 (1983), 139–71. xx, xxi, 398, 411, 421Google Scholar
Braun, R. B., A Gelfand–Neumark theorem for C -alternative algebras. Math. Z. 185 (1984), 225–42. xx, xxi, 411Google Scholar
Braun, R. B., Kaup, W., and Upmeier, H., A holomorphic characterization of Jordan C -algebras. Math. Z. 161 (1978), 277–90. 210Google Scholar
Brelot, M., Points irréguliers et transformations continues en théorie du potentiel. J. Math. Pures Appl. 19 (1940), 319–37.Google Scholar
Brelot, M., Sur les ensembles effilés. Bull. Sci. Math. 68 (1944), 1236.Google Scholar
Bremner, M. and Hentzel, I., Identities for algebras obtained from the Cayley–Dickson process. Comm. Algebra 29 (2001), 3523–34.Google Scholar
Brešar, M., Cabrera, M., Fosner, M., and Villena, A. R., Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan–Banach algebras. Studia Math. 169 (2005), 207–28. 602Google Scholar
Brešar, M., Šemrl, P., and Špenko, S., On locally complex algebras and low-dimensional Cayley–Dickson algebras. J. Algebra 327 (2011), 107–25.Google Scholar
Browder, A., States, numerical ranges, etc.. In Proceedings of the Brown informal analysis seminar. Summer, 1969 (revised version, Summer of 2012).Google Scholar
Browder, A., On Bernstein’s inequality and the norm of Hermitian operators. Amer. Math. Monthly 78 (1971), 871–3.Google Scholar
Brown, R., On generalized Cayley–Dickson algebras. Pacific J. Math. 20 (1967), 415–22.Google Scholar
Bunce, L. J., Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., A Saitô–Tomita– Lusin theorem for JB -triples and applications. Quart. J. Math. Oxford 57 (2006), 3748.Google Scholar
Bunce, L. J. and Peralta, A. M., Images of contractive projections on operator algebras. J. Math. Anal. Appl. 272 (2002), 5566. 210CrossRefGoogle Scholar
Burgos, M. J., Peralta, A. M., Ramírez, M. I., and Ruiz, E. E., Von Neumann regularity in Jordan–Banach triples. In [704], pp. 67–88.Google Scholar
Busby, R. C., Double centralizers and extensions of C -algebras. Trans. Amer. Math. Soc. 132 (1968), 7999.Google Scholar
Cabello, F., Regards sur le problème des rotations de Mazur. Extracta Math. 12 (1997), 97116.Google Scholar
Cabrera, M., El Marrakchi, A., Martínez, J., and Rodríguez, A., An Allison– Kantor–Koecher–Tits construction for Lie H -algebras. J. Algebra 164 (1994), 361408. xxv, 556Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Malcev H -algebras. Math. Proc. Cambridge Phil. Soc. 103 (1988), 463–71. xxv, 553, 554Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Nonassociative real H -algebras. Publ. Mat. 32 (1988), 267–74. xxiv, 549, 551Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., A note on real H -algebras. Math. Proc. Cambridge Phil. Soc. 105 (1989), 131–2.CrossRefGoogle Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Structurable H -algebras. J. Algebra 147 (1992), 1962. xxv, 552, 553, 555, 556Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., Normed versions of the Zel’manov prime theorem: positive results and limits. In: Operator theory, operator algebras and related topics (Timisoara, 1996) (eds. Gheondea, A., Gologan, R. N. and Timotin, D.), Theta Found., Bucharest, 1997, pp. 6577. 462, 463, 465Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., Zel’manov’s theorem for primitive Jordan–Banach algebras. J. London Math. Soc. 57 (1998), 231–44. xxii, 463, 464, 465Google Scholar
Cabrera, M., Moreno, A., Rodríguez, A., and Zel’manov, E. I., Jordan polynomials can be analytically recognized. Studia Math. 117 (1996), 137–47. xxii, 437, 470Google Scholar
Cabrera, M. and Rodríguez, A., Extended centroid and central closure of semiprime normed algebras: a first approach. Comm. Algebra 18 (1990), 2293–326. xxiii, 408, 546, 555Google Scholar
Cabrera, M. and Rodríguez, A., Nonassociative ultraprime normed algebras. Quart. J. Math. Oxford 43 (1992), 17. xxi, xxiii, 409, 546Google Scholar
Cabrera, M. and Rodríguez, A., New associative and nonassociative Gelfand–Naimark theorems. Manuscripta Math. 79 (1993), 197208.Google Scholar
Cabrera, M. and Rodríguez, A., Zel’manov theorem for normed simple Jordan algebras with a unit. Bull. London Math. Soc. 25 (1993), 5963. xxii, 467, 468Google Scholar
Cabrera, M. and Rodríguez, A., Non-degenerately ultraprime Jordan–Banach algebras: a Zel’manovian treatment. Proc. London Math. Soc. 69 (1994), 576604. xxii, 409, 468, 469Google Scholar
Cabrera, M. and Rodríguez, A., A new simple proof of the Gelfand–Mazur–Kaplansky theorem. Proc. Amer. Math. Soc. 123 (1995), 2663–6. 408Google Scholar
Cabrera, M. and Rodríguez, A., On the Gelfand–Naimark axiom ‖a a‖ = ‖a ‖‖a. Quart. J. Math. Oxford 63 (2012), 855–60.Google Scholar
Calderón, A., Kaidi, A., Martín, C., Morales, A., Ramírez, M., and Rochdi, A., Finite-dimensional absolute-valued algebras. Israel J. Math. 184 (2011), 193220.Google Scholar
Calderón, A. J. and Martín, C., Two-graded absolute valued algebras. J. Algebra 292 (2005), 492515.Google Scholar
Calkin, J. W., Two-sided ideals and congruences in the ring of bounded operators in Hilbert space. Ann. of Math. 42 (1941), 839–73.Google Scholar
Caradus, S. R., Operators of Riesz type. Pacific J. Math. 18 (1966), 6171.Google Scholar
Cartan, E., Les groupes bilinéaires et les systèmes de nombres complexes. Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 12 (1898), 199. Reprinted in Oeuvres Complètes, Vol II, Paris, Gauthier-Villars, 1952.Google Scholar
Cartan, H., Théorie générale du balayage en potentiel newtonien. Ann. Univ. Grenoble. Sect. Sci. Math. Phys. 22 (1946), 221–80.Google Scholar
Casazza, P. G., Approximation properties. In Handbook of the geometry of Banach spaces, Vol. I (eds. Johnson, W. B. and Lindenstrauss, J.), pp. 271316, North-Holland, Amsterdam, 2001. Addenda and corrigenda: In [757], pp. 1817–18.Google Scholar
Castellón, A. and Cuenca, J. A., Isomorphisms of H -triple systems. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 19 (1992), 507–14. 561Google Scholar
Castellón, A. and Cuenca, J. A., Associative H -triple systems. In [734], pp. 45–67. 551, 561Google Scholar
Cayley, A., On Jacobi’s elliptic functions, in reply to the Rev. B. Bronwin; and on quaternions. Philos. Mag. 26 (1845), 208–11.Google Scholar
Cedilnik, A. and Rodríguez, A., Continuity of homomorphisms into complete normed algebraic algebras. J. Algebra 264 (2003), 614. 595, 596Google Scholar
Cedilnik, A. and Zalar, B., Nonassociative algebras with submultiplicative bilinear form. Acta Math. Univ. Comenian. 63 (1994), 285301.Google Scholar
Chan, K.-C. and Dokovic, D. Z., Conjugacy classes of subalgebras of the real sedenions. Canad. Math. Bull. 49 (2006), 492507.Google Scholar
Chandid, A. and Rochdi, A., Mutations of absolute valued algebras. Int. J. Algebra 2 (2008), 357–68.Google Scholar
Choi, M. D. and Effros, E., Injectivity and operator spaces. J. Funct. Anal. 24 (1974), 156209.Google Scholar
Chonghu, W., Some geometric properties of Banach spaces and x+λy‖−‖x λ on it. J. Nanjing Univ. 6 (1989), 3745.Google Scholar
Chu, C.-H., Dang, T., Russo, B., and Ventura, B., Surjective isometries of real C -algebras. J. London Math. Soc. 47 (1993), 97118.Google Scholar
Chu, C.-H., Iochum, B., and Loupias, G., Grothendieck’s theorem and factorization of operators in Jordan triples. Math. Ann. 284 (1989), 4153. xix, 2, 245, 267, 343, 344, 346Google Scholar
Chu, C.-H. and Mellon, P., Jordan structures in Banach spaces and symmetric manifolds. Expos. Math. 16 (1998), 157–80. 211Google Scholar
Chu, C.-H. and Velasco, M. V., Automatic continuity of homomorphisms in nonassociative Banach algebras. Canadian J. Math. 65 (2013), 9891004.Google Scholar
Civin, P. and Yood, B., Lie and Jordan structures in Banach algebras. Pacific J. Math. 15 (1965), 775–97. 583Google Scholar
Cleveland, S. B., Homomorphisms of non-commutative ∗-algebras. Pacific J. Math. 13 (1963), 1097–109.Google Scholar
Cobalea, M. A. and Fernández, A., Prime noncommutative Jordan algebras and central closure. Algebras Groups Geom. 5 (1988), 129–36. 408Google Scholar
Cohn, P. M., On homomorphic images of special Jordan algebras. Canadian J. Math. 6 (1954), 253–64.Google Scholar
Contreras, M. D. and Payá, R., On upper semicontinuity of duality mappings. Proc. Amer. Math. Soc. 121 (1994), 451–9.Google Scholar
Contreras, M. D., Payá, R., and Werner, W., C -algebras that are I-rings. J. Math. Anal. Appl. 198 (1996), 227–36.Google Scholar
Cowie, E. R., An analytic characterization of groups with no finite conjugacy classes. Proc. Amer. Math. Soc. 87 (1983), 710.Google Scholar
Crabb, M. J., Duncan, J., and McGregor, C. M., Some extremal problems in the theory of numerical ranges. Acta Math. 128 (1972), 123–42.Google Scholar
Crabb, M. J., Duncan, J., and McGregor, C. M., Characterizations of commutativity for C -algebras. Glasgow Math. J. 15 (1974), 172–5. 400Google Scholar
Crabb, M. J. and McGregor, C. M., Numerical ranges of powers of Hermitian elements. Glasgow Math. J. 28 (1986), 3745.Google Scholar
Crabb, M. J. and McGregor, C. M., Polynomials in a Hermitian element. Glasgow Math. J. 30 (1988), 171–6.Google Scholar
Cuartero, B. and Galé, J. E., Locally PI-algebras over valued fields. In Aportaciones Matemáticas en Memoria del Profesor V. M. Onieva, pp. 137–45, Santander, Universidad de Cantabria, 1991.Google Scholar
Cuartero, B. and Galé, J. E., Bounded degree of algebraic topological algebras. Comm. Algebra 422 (1994), 329–37.Google Scholar
Cuartero, B., Galé, J. E., Rodríguez, A., and Slinko, A. M., Bounded degree of weakly algebraic topological Lie algebras. Manuscripta Math. 81 (1993), 129–39. 658Google Scholar
Cudia, D. F., The geometry of Banach spaces. Smoothness. Trans. Amer. Math. Soc. 110 (1964), 284314.Google Scholar
Cuenca, J. A., On one-sided division infinite-dimensional normed real algebras. Publ. Mat. 36 (1992), 485–8.Google Scholar
Cuenca, J. A., On composition and absolute-valued algebras. Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), 717–31.Google Scholar
Cuenca, J. A., On an Ingelstam’s theorem. Comm. Algebra 35 (2007), 4057–67.Google Scholar
Cuenca, J. A., On structure theory of pre-Hilbert algebras. Proc. R. Soc. Edinburgh 139A (2009), 303–19.Google Scholar
Cuenca, J. A., Some classes of pre-Hilbert algebras with norm-one central idempotent. Israel J. Math. 193 (2013), 343–58.Google Scholar
Cuenca, J. A., A new class of division algebras and Wedderburn’s and Frobenius’ Theorems. Preprint 2012.Google Scholar
Cuenca, J. A., Third-power associative absolute vaued algebras with a nonzero idempotent commuting with all idempotents. Publ. Mat. 58 (2014), 469–84.Google Scholar
Cuenca, J. A., García, A., and Martín, C.. Structure theory for L -algebras, Math. Proc. Cambridge Phil. Soc. 107 (1990), 361–5. xxv, 554Google Scholar
Cuenca, J. A. and Rodríguez, A., Isomorphisms of H -algebras. Math. Proc. Cambridge Phil. Soc. 97 (1985), 93–9. xxiv, 546, 549Google Scholar
Cuenca, J. A. and Rodríguez, A., Structure theory for noncommutative Jordan H -algebras. J. Algebra 106 (1987), 114. xxiii, xxv, 545, 552, 553Google Scholar
Cuenca, J. A. and Rodríguez, A., Absolute values on H -algebras. Comm. Algebra 23 (1995), 1709–40. 481Google Scholar
Cuntz, J., Locally C -equivalent algebras. J. Funct. Anal. 23 (1976), 95106.Google Scholar
Cusack, J. M., Jordan derivations on rings. Proc. Amer. Math. Soc. 53 (1975), 321–4.Google Scholar
Dales, H. G., Norming nil algebras. Proc. Amer. Math. Soc. 83 (1981), 71–4.Google Scholar
Dales, H. G., On norms on algebras. In [773], pp. 61–96.Google Scholar
Dang, T., Real isometries between JB -triples. Proc. Amer. Math. Soc. 114 (1992), 971–80.Google Scholar
Dang, T. and Russo, B., Real Banach Jordan triples. Proc. Amer. Math. Soc. 122 (1994), 135–45.Google Scholar
Darpö, E. and Rochdi, A., Classification of the four-dimensional power-commutative real division algebras. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), 1207–23.Google Scholar
Davis, W. J., Separable Banach spaces with only trivial isometries. Rev. Roumaine Math. Pures Appl. 16 (1971), 1051–4.Google Scholar
Davis, W. J., Figiel, T., Johnson, W. B., and Pełczyński, A., Factoring weakly compact operators. J. Funct. Anal. 17 (1974), 311–27.Google Scholar
Diankha, O., Diouf, A., and Rochdi, A., A brief statement on the absolute-valued algebras with one-sided unit. Int. J. Algebra 7 (2013), 833–8.Google Scholar
Dickson, L. E., On quaternions and their generalization and the history of the eight square theorem. Ann. of Math. 20 (1919), 155–71.Google Scholar
Dickson, L. E., Linear algebras with associativity not assumed. Duke Math. J. 1 (1935), 113–25.Google Scholar
Dineen, S., The second dual of a JB -triple system. In Complex Analysis, Functional Analysis and Approximation Theory (ed. Múgica, J.), pp. 67–9, North-Holland Math. Stud. 125, North-Holland, Amsterdam–New York, 1986. xix, 2, 211, 236, 241Google Scholar
Doran, R. S., A generalization of a theorem of Civin and Yood on Banach ∗-algebras. Bull. London Math. Soc. 4 (1972), 25–6.Google Scholar
Dorofeev, G. V., An example of a solvable but not nilpotent alternative ring. Uspekhi Mat. Nauk 15 (1960), 147–50.Google Scholar
Duncan, J., Review of [425]. Math. Rev. 87e:46067.Google Scholar
Duncan, J., McGregor, C. M., Pryce, J. D., and White, A. J., The numerical index of a normed space. J. London Math. Soc. 2 (1970), 481–8.Google Scholar
Duncan, J. and Taylor, P. J., Norm inequalities for C -algebras. Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), 119–29. 400Google Scholar
Dunford, N., Spectral theory I. Convergence to projections. Trans. Amer. Math. Soc. 54 (1943), 185217.Google Scholar
Dutta, S. and Rao, T. S. S. R. K., Norm-to-weak upper semi-continuity of the pre-duality map. J. Anal. 12 (2005), 110.Google Scholar
Eakin, P. and Sathaye, A., On automorphisms and derivations of Cayley–Dickson algebras. J. Algebra 129 (1990), 263–78.Google Scholar
Edwards, C. M., On Jordan W -algebras. Bull. Sci. Math. 104 (1980), 393403. xix, xx, 2, 19Google Scholar
Edwards, C. M., Multipliers of JB-algebras. Math. Ann. 249 (1980), 265–72.Google Scholar
Edwards, C. M., Fernández-Polo, F. J., Hoskin, C. S., and Peralta, A. M., On the facial structure of the unit ball in a JB -triple. J. Reine Angew. Math. 641 (2010), 123–44.Google Scholar
Edwards, C. M. and Rüttimann, G. T., On the facial structure of the unit balls in a JBW -triple and its predual. J. London Math. Soc. 38 (1988), 317–32.Google Scholar
Edwards, C. M. and Rüttimann, G. T., The facial and inner ideal structure of a real JBW -triple. Math. Nachr. 222 (2001), 159–84.Google Scholar
Edwards, R. E., Multiplicative norms on Banach algebras. Math. Proc. Cambridge Phil. Soc. 47 (1951), 473–4.Google Scholar
Effros, E. G. and Størmer, E., Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc. 127 (1967), 313–16.Google Scholar
Effros, E. G. and Størmer, E., Positive projections and Jordan structure in operator algebras. Math. Scand. 45 (1979), 127–38. 210Google Scholar
Eidelheit, M., On isomorphisms of rings of linear operators. Studia Math. 9 (1940), 97105.Google Scholar
Eilenberg, S., Extensions of general algebras. Ann. Soc. Polon. Math. 21 (1948), 125–34.Google Scholar
Elduque, A. and Pérez, J. M., Infinite-dimensional quadratic forms admitting composition. Proc. Amer. Math. Soc. 125 (1997), 2207–16.Google Scholar
Ellis, A. J., The duality of partially ordered normed linear spaces. J. London Math. Soc. 39 (1964), 730–44.Google Scholar
Ellis, A. J., Minimal decompositions in base normed spaces. In Foundations of quantum mechanics and ordered linear spaces (Advanced Study Inst., Marburg, 1973), pp. 30–2. Lecture Notes in Phys. 29, Springer, Berlin, 1974.Google Scholar
El-Mallah, M. L., Quelques résultats sur les algèbres absolument valuées. Arch. Math. 38 (1982), 432–7.Google Scholar
El-Mallah, M. L., Sur les algèbres absolument valuées qui vérifient l’identité (x, x, x)=0. J. Algebra 80 (1983), 314–22.Google Scholar
El-Mallah, M. L., On finite dimensional absolute valued algebras satisfying (x, x, x)=0. Arch. Math. 49 (1987), 1622.Google Scholar
El-Mallah, M. L., Absolute valued algebras with an involution. Arch. Math. 51 (1988), 3949.Google Scholar
El-Mallah, M. L., Absolute valued algebras containing a central idempotent. J. Algebra 128 (1990), 180–7.Google Scholar
El-Mallah, M. L., Absolute valued algebraic algebra satisfying (x, x, x) = 0. Pure Math. Appl. 8 (1997), 3952.Google Scholar
El-Mallah, M. L., Semi-algebraic absolute valued algebras with an involution. Comm. Algebra 31 (2003), 3135–41.Google Scholar
El-Mallah, M. L., Elgendy, H., Rochdi, A., and Rodríguez, A., On absolute valued algebras with involution. Linear Algebra Appl. 414 (2006), 295303.Google Scholar
El-Mallah, M. L. and Micali, A., Sur les algèbres normées sans diviseurs topologiques de zéro. Bol. Soc. Mat. Mexicana 25 (1980), 23–8.Google Scholar
El-Mallah, M. L. and Micali, A., Sur les dimensions des algèbres absolument valuées. J. Algebra 68 (1981), 237–46.Google Scholar
Enflo, P., A counterexample to the approximation problem in Banach spaces. Acta Math. 130 (1973), 309–17.Google Scholar
Erickson, T. S., Martindale, W. S. III, and Osborn, J. M., Prime nonassociative algebras. Pacific J. Math. 60 (1975), 4963. 495Google Scholar
Esterle, J., Normes d’algèbres minimales, topologie d’algèbre normée minimum sur certaines algèbres d’endomorphismes continus d’un espace normé. C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A425–7.Google Scholar
Fan, K. and Glicksberg, I., Some geometrical properties of the spheres in a normed linear space. Duke Math. J. 25 (1958), 553–68.Google Scholar
Feldman, K. E., New proof of Frobenius hypothesis on the dimensions of real algebras without divisors of zero. Moscow Univ. Math. Bull. 55 (2000), 4850.Google Scholar
Fernández, A., Modular annihilator Jordan algebras. Comm. Algebra 13 (1985), 2597–613. 598Google Scholar
Fernández, A., Noncommutative Jordan Riesz algebras. Quart. J. Math. Oxford 39 (1988), 6780. 598, 599Google Scholar
Fernández, A., Noncommutative Jordan algebras containing minimal inner ideals. In [749], pp. 153–76.Google Scholar
Fernández, A., Banach–Lie algebras spanned by extremal elements. In [704], pp. 125–32. 598Google Scholar
Fernández, A., Banach–Lie algebras with extremal elements. Quart. J. Math. Oxford 62 (2011), 115–29. 598Google Scholar
Fernández, A., García, E., and Rodríguez, A., A Zel’manov prime theorem for JB -algebras. J. London Math. Soc. 46 (1992), 319–35. xxi, xxii, 405, 408, 437, 466, 467Google Scholar
Fernández, A., García, E., and Sánchez, E., von Neumann regular Jordan Banach triple systems. J. London Math. Soc. 42 (1990), 3248. 599, 600Google Scholar
Fernández, A. and Rodríguez, A., Primitive noncommutative Jordan algebras with nonzero socle. Proc. Amer. Math. Soc. 96 (1986), 199206. 598Google Scholar
Fernández, A. and Rodríguez, A., On the socle of a noncommutative Jordan algebra. Manuscripta Math. 56 (1986), 269–78. 598Google Scholar
Fernández, A. and Rodríguez, A., A Wedderburn theorem for nonassociative complete normed algebras. J. London Math. Soc. 33 (1986), 328–38. xxv, 548, 583, 584, 585Google Scholar
Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., Surjective isometries between real JB -triples. Math. Proc. Cambridge Phil. Soc. 137 (2004), 709–23.Google Scholar
Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., Geometric characterization of tripotents in real and complex JB -triples. J. Math. Anal. Appl. 295 (2004), 435–43.Google Scholar
Fernández-Polo, F. J., Garcés, J. J., and Peralta, A. M., A Kaplansky theorem for JB -triples. Proc. Amer. Math. Soc. 140 (2012), 3179–91.Google Scholar
Finet, C., Uniform convexity properties of norms on superreflexive Banach spaces. Israel J. Math. 53 (1986), 8192.Google Scholar
Foias, C., Sur certains theoremes de J. von Neumann concernant les ensembles spectraux. Acta Sci. Math. 18 (1957), 1520.Google Scholar
Ford, J. W. M., A square root lemma for Banach ∗-algebras. J. London Math. Soc. 42 (1967), 521–2.Google Scholar
Formanek, E., The Nagata–Higman Theorem. Acta Appl. Math. 21 (1990), 185–92.Google Scholar
Franchetti, C., Lipschitz maps and the geometry of the unit ball in normed spaces. Arch. Math. 46 (1986), 7684.Google Scholar
Franchetti, C. and Payá, R., Banach spaces with strongly subdifferentiable norm. Boll. Un. Mat. Ital. 7 (1993), 4570.Google Scholar
Friedman, Y. and Russo, B., Structure of the predual of a JBW -triple. J. Reine Angew. Math. 356 (1985), 6789. 236, 274, 332, 337Google Scholar
Friedman, Y. and Russo, B., The Gelfand–Naimark theorem for JB -triples. Duke Math. J. 53 (1986), 139–48. xxii, 459Google Scholar
Frobenius, F. G., Über lineare Substitutionen und bilineare Formen. J. Reine Angew. Math. 84 (1878), 163. Reprinted in Gesammelte Abhandlungen Band I, pp. 343–405.Google Scholar
Froelich, J., Unital multiplications on a Hilbert space. Proc. Amer. Math. Soc. 117 (1993), 757–9.Google Scholar
Fukamiya, M., On a theorem of Gelfand and Neumark and the B -algebra. Kumamoto J. Sci. Ser. A 1 (1952), 1722. 686Google Scholar
Fuster, R. and Marquina, A., Geometric series in incomplete normed algebras. Amer. Math. Monthly 91 (1984), 4951.Google Scholar
Galé, J. E., Weakly compact homomorphisms in nonassociative algebras. In [734], pp. 167–71.Google Scholar
Galé, J. E., Ransford, T. J., and White, M. C., Weakly compact homomorphisms. Trans. Amer. Math. Soc. 331 (1992), 815–24. 336Google Scholar
Galina, E., Kaplan, A., and Saal, L., Charged representations of the infinite Fermi and Clifford algebras. Lett. Math. Phys. 72 (2005), 6577.Google Scholar
Galina, E., Kaplan, A., and Saal, L., Spinor types in infinite dimensions. J. Lie Theory 15 (2005), 457–95.Google Scholar
Gantmacher, V., Über schwache totalstetige Operatoren. Rec. Math. [Mat. Sbornik] 7 (1940), 301–8.Google Scholar
Gardner, L. T., On isomorphisms of C -algebras. Amer. J. Math. 87 (1965), 384–96.Google Scholar
Gardner, L. T., An elementary proof of the Russo–Dye theorem. Proc. Amer. Math. Soc. 90 (1984), 181.Google Scholar
Garibaldi, S. and Petersson, H. P., Wild Pfister forms over Henselian fields, K-theory, and conic division algebras. J. Algebra 327 (2011), 386465.Google Scholar
Gelfand, I. M., Abstrakte Funktionen und lineare Operatoren, Mat. Sb. 4 (1938), 235–86.Google Scholar
Gelfand, I. M., Normierte Ringe. Rec. Math. [Mat. Sbornik]9 (1941), 324.Google Scholar
Gelfand, I. M. and Naimark, M. A., On the embedding of normed rings into the ring of operators in Hilbert space. Mat. Sbornik 12 (1943), 197213.Google Scholar
Gelfand, I. M. and Kolmogorov, A. N., Rings of continuous functions on topological spaces. Doklady Akad. Nauk SSSR 22 (1939), 1115.Google Scholar
Giles, J. R., Gregory, D. A., and Sims, B., Geometrical implications of upper semi-continuity of the duality mapping of a Banach space. Pacific J. Math. 79 (1978), 99109.Google Scholar
Gleichgewicht, B., A remark on absolute-valued algebras. Colloq. Math. 11 (1963), 2930.Google Scholar
Glickfeld, B. W., A metric characterization of C(X) and its generalization to C -algebras. Illinois J. Math. 10 (1966), 547–56.Google Scholar
Glimm, J. G. and Kadison, R. V., Unitary operators in C -algebras. Pacific J. Math. 10 (1960), 547–56.Google Scholar
Godefroy, G. and Indumathi, V., Norm-to-weak upper semi-continuity of the duality and pre-duality mappings. Set-Valued Anal. 10 (2002), 317–30.Google Scholar
Godefroy, G., Montesinos, V., and Zizler, V., Strong subdifferentiability of norms and geometry of Banach spaces. Comment. Math. Univ. Carolinae 36 (1995), 493502.Google Scholar
Godefroy, G. and Rao, T. S. S. R. K., Renorming and extremal structures. Illinois J. Math. 48 (2004), 1021–9.Google Scholar
Gohberg, I. C., Markus, A. S., and Fel’dman, I. A., Normally solvable operators and ideals associated with them. Bul. Akad. Stiince RSS Moldoven 10 (1960), 5170. Amer. Math. Soc. Transl. 61 (1967), 63–4.Google Scholar
Golod, E. S., On nil-algebras and finitely approximable p-groups. Izv. Akad. Nauk SSSR, Ser. Mat. 28 (1964), 273–6. 633Google Scholar
Gorin, E. A., Bernstein inequalities from the perspective of operator theory. (In Russian.) Vestnik Khar’kov. Gos. Univ. 205 (1980), 77105, 140.Google Scholar
Gowers, W. T. and Maurey, B., The unconditional basic sequence problem. J. Amer. Math. Soc. 6 (1993), 851–74.Google Scholar
Grabiner, S., The nilpotence of Banach nil algebras. Proc. Amer. Math. Soc. 21 (1969), 510.Google Scholar
Gregory, D. A., Upper semi-continuity of subdifferential mappings. Canad. Math. Bull. 23 (1980), 1119.Google Scholar
Greim, P. and Rajalopagan, M., Almost transitivity in C 0(L). Math. Proc. Cambridge Phil. Soc. 121 (1997), 7580.Google Scholar
Grzaślewicz, R. and Scherwentke, P., On strongly extreme and denting contractions in L (C(X), C(Y)). Bull. Acad. Sinica 25 (1997), 155–60.Google Scholar
Haagerup, U., Kadison, R. V., and Pedersen, G. K., Means of unitary operators, revisited. Math. Scand. 100 (2007), 193–7.Google Scholar
Haïly, A., A non-semiprime associative algebra with zero weak radical. Extracta Math. 12 (1997), 5360.Google Scholar
Haïly, A., Kaidi, A., and Rodríguez, A., Algebra descent spectrum of operators. Israel J. Math. 177 (2010), 349–68.Google Scholar
Hamana, M., Injective envelopes of C -algebras. J. Math. Soc. Japan 31 (1979), 181–97.Google Scholar
Hamilton, W. R., Note by Professor Sir W. R. Hamilton, respecting the researches of John T. Graves, esq. Trans. R. Irish Acad., 1848, Science 338–41.Google Scholar
Hammoudi, L., Nil-algebras and infinite groups. J. Math. Sci. (NY) 144 (2007), 4004–12.Google Scholar
Hanche-Olsen, H., A note on the bidual of a JB-algebra. Math. Z. 175 (1980), 2931.Google Scholar
Hansen, M. L. and Kadison, R. V., Banach algebras with unitary norms. Pacific J. Math. 175 (1996), 535–52.Google Scholar
Hansen, F. and Pedersen, G. K., Jensen’s inequality for operators and Löwner’s theorem. Math. Ann. 258 (1981/82), 229–41.Google Scholar
Harmand, P. and Rao, T. S. S. R. K., An intersection property of balls and relations with M-ideals. Math. Z. 197 (1988), 277–90.Google Scholar
Harris, L. A., The numerical range of holomorphic functions in Banach spaces. Amer. J. Math. 93 (1971), 1005–19.Google Scholar
Harris, L. A., Banach algebras with involution and Möbius transformations. J. Funct. Anal. 11 (1972), 116.Google Scholar
Harris, L. A., Bounded symmetric homogeneous domains in infinite dimensional spaces. In Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973), pp. 1340. Lecture Notes in Math. 364, Springer, Berlin, 1974. 210, 211Google Scholar
Harris, L. A., The numerical range of functions and best approximation. Math. Proc. Cambridge Philos. Soc. 76 (1974), 133–41.Google Scholar
Harris, L. A. and Kadison, R. V., Schurian algebras and spectral additivity. J. Algebra 180 (1996), 175–86.Google Scholar
Harte, R. and Mbekhta, M., On generalized inverses in C -algebras. Studia Math. 103 (1992), 71–7.Google Scholar
Heinrich, S., Ultraproducts in Banach space theory. J. Reine Angew. Math. 313 (1980), 72104. 211, 236Google Scholar
Hejazian, S. and Niknam, A., A Kaplansky theorem for JB -algebras. Rocky Mountain J. Math. 28 (1998), 977–82.Google Scholar
Herstein, I. N., Jordan homomorphism. Trans. Amer. Math. Soc. 81 (1956), 331–41.Google Scholar
Herstein, I. N., Jordan derivations of prime rings. Proc. Amer. Math. Soc. 8 (1957), 1104–10.Google Scholar
Hessenberger, G., A spectral characterization of the socle of Banach Jordan systems. Math. Z. 223 (1996), 561–8. 603Google Scholar
Hessenberger, G., Inessential and Riesz elements in Banach Jordan systems. Quart. J. Math. Oxford 47 (1996), 337–47. 603Google Scholar
Hessenberger, G., The trace in Banach Jordan pairs. Bull. London Math. Soc. 30 (1998), 561–8. 603Google Scholar
Hessenberger, G., An improved characterization of inessential elements in Banach Jordan systems and the generalized Ruston characterization. Arch. Math. (Basel) 74 (2000), 438–40. 603Google Scholar
Hessenberger, G. and Maouche, A., On Banach Jordan systems with at most two spectral values. Far East J. Math. Sci. (FJMS) 7 (2002), 115–20. 603Google Scholar
Hirschfeld, R. A. and Johnson, B. E., Spectral characterization of finite-dimensional algebras. Indag. Math. 34 (1972), 1923. 596Google Scholar
Hogben, L. and McCrimmon, K., Maximal modular inner ideals and the Jacobson radical of a Jordan algebra. J. Algebra 68 (1981), 155–69.Google Scholar
Holsztynski, W., Continuous mappings induced by isometries of spaces of continuous functions. Studia Math. 26 (1966), 133–6.Google Scholar
Horn, G., Classification of JBW -triples of Type I. Math. Z. 196 (1987), 271–91. xxii, 340, 344, 438, 459Google Scholar
Horn, G., Coordinatization theorem for JBW -triples. Quart. J. Math. Oxford 38 (1987), 321–35. xxi, 411, 416Google Scholar
Huang, X.-J. and Ng, C.-K., An abstract characterization of unital operator spaces. J. Operator Theory 67 (2012), 289–98.Google Scholar
Huruya, T., The normed space numerical index of C -algebras. Proc. Amer. Math. Soc. 63 (1977), 289–90.Google Scholar
Hurwitz, A., Über die Composition der quadratischen Formen von beliebig vielen Variabelm. Nach. Ges. Wiss. Göttingen (1898), 309–16.Google Scholar
Imaeda, K. and Imaeda, M., Sedenions: algebra and analysis. Appl. Math. Comp. 115 (2000), 7788.Google Scholar
Ingelstam, L., A vertex property for Banach algebras with identity, Math. Scand. 11 (1962), 2232.Google Scholar
Ingelstam, L., Hilbert algebras with identity. Bull. Amer. Math. Soc. 69 (1963), 794–6.Google Scholar
Ingelstam, L., Non-associative normed algebras and Hurwitz’ problem. Ark. Mat. 5 (1964), 231–8.Google Scholar
Ingelstam, L., Real Banach algebras. Ark. Mat. 5 (1964), 239–79.Google Scholar
Iochum, B., Loupias, G, and Rodríguez, A., Commutativity of C -algebras and associativity of JB -algebras. Math. Proc. Cambridge Phil. Soc. 106 (1989), 281–91. xxi, 398, 399, 400, 401Google Scholar
Isidro, J. M., Kaup, W., and Rodríguez, A., On real forms of JB -triples. Manuscripta Math. 86 (1995), 311–35. 242, 243, 459Google Scholar
Isidro, J. M. and Rodríguez, A., Isometries of JB-algebras. Manuscripta Math. 86 (1995), 337–48.Google Scholar
Isidro, J. M. and Rodríguez, A., On the definition of real W*-algebras. Proc. Amer. Math. Soc. 124 (1996), 3407–10. 244Google Scholar
Jacobson, N., Structure theory of simple rings without finiteness assumptions. Trans. Amer. Math. Soc. 57 (1945), 228–45.Google Scholar
Jacobson, N., The radical and semisimplicity for arbitrary rings. Amer. J. Math. 67 (1945), 300–20.Google Scholar
Jacobson, N., A topology for the set of primitive ideals in an arbitrary ring. Proc. Nat. Acad. Sci. USA 31 (1945), 333–8.Google Scholar
Jacobson, N., Structure theory for algebraic algebras of bounded degree. Ann. of Math. 46 (1945), 695707.Google Scholar
Jacobson, N., A theorem on the structure of Jordan algebras. Proc. Nat. Acad. Sci. USA 42 (1956), 140–7.Google Scholar
Jacobson, N., Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo 7 (1958), 5580.Google Scholar
Jacobson, N., Abraham Adrian Albert 1905–1972. Bull. Amer. Math. Soc. 80 (1974), 1075–100. Reprinted in [691], pp. xlv–lxiii. 546Google Scholar
Jacobson, N. and Rickart, C. E., Jordan homomorphisms of rings. Trans. Amer. Math. Soc. 69 (1950), 479502.Google Scholar
Johnson, B. E., Centralisers on certain topological algebras. J. London Math. Soc. 39 (1964), 603–14.Google Scholar
Johnson, B. E., The uniqueness of the (complete) norm topology. Bull. Amer. Math. Soc. 73 (1967), 537–9. 596Google Scholar
Johnson, B. E., Continuity of derivations on commutative Banach algebras. Amer. J. Math. 91 (1969), 110.Google Scholar
Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky. Amer. J. Math. 90 (1968), 1067–73. 466, 548, 596Google Scholar
Jordan, P., von Neumann, J., and Wigner, E., On an algebraic generalization of the quantum mechanical formalism. Ann. of Math. 35 (1934), 2964.Google Scholar
Kadets, V., Katkova, O., Martín, M., and Vishnyakova, A., Convexity around the unit of a Banach algebra. Serdica Math. J. 34 (2008), 619–28.Google Scholar
Kadison, R. V., Isometries of operator algebras. Ann. of Math. 54 (1951), 325–38.Google Scholar
Kadison, R. V., A generalized Schwarz inequality and algebraic invariants for operator algebras. Ann. of Math. 56 (1952), 494503.Google Scholar
Kadison, R. V. and Pedersen, G. K., Means and convex combinations of unitary operators. Math. Scand. 57 (1985), 249–66.Google Scholar
Kaidi, A., Structure des algèbres de Jordan–Banach non commutatives reelles de division. In [749], pp. 119–24. 597Google Scholar
Kaidi, A., Martínez, J., and Rodríguez, A., On a non-associative Vidav–Palmer theorem. Quart. J. Math. Oxford 32 (1981), 435–42.Google Scholar
Kaidi, A., Morales, A, and Rodríguez, A., Prime non-commutative JB -algebras. Bull. London Math. Soc. 32 (2000), 703–8. xxii, 421Google Scholar
Kaidi, A., Morales, A., and Rodríguez, A., Geometrical properties of the product of a C -algebra. Rocky Mountain J. Math. 31 (2001), 197213.Google Scholar
Kaidi, A., Morales, A, and Rodríguez, A., A holomorphic characterization of C - and JB -algebras. Manuscripta Math. 104 (2001), 467–78. xviii, 272, 273Google Scholar
Kaidi, A., Morales, A., and Rodríguez, A., Non-associative C -algebras revisited. In [1141], pp. 379–408. xx, 275, 330, 346, 421, 422Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Absolute-valued algebraic algebras are finite-dimensional. J. Algebra 195 (1997), 295307.Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Absolute-valued algebraic algebras. In [705], pp. 103–9.Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Nearly absolute-valued algebras. Comm. Algebra 30 (2002), 3267–84.Google Scholar
Kaidi, A. and Sánchez, A., J-diviseurs topologiques de zéro dans une algèbre de Jordan n.c. normée. In [733], pp. 193–7. 597Google Scholar
Kamowitz, H. and Scheinberg, S., The spectrum of automorphisms of Banach algebras. J. Funct. Anal. 4 (1969), 268–76.Google Scholar
Kaplansky, I., Topological rings. Amer. J. Math. 69 (1947), 153–83.Google Scholar
Kaplansky, I., Topological methods in valuation theory. Duke Math. J. 14 (1947), 527–41.Google Scholar
Kaplansky, I., Dual rings. Ann. of Math. 49 (1948), 689701. xxv, 551, 584Google Scholar
Kaplansky, I., Normed algebras. Duke Math. J. 16 (1949), 399418. 584Google Scholar
Kaplansky, I., Topological representation of algebras II. Trans. Amer. Math. Soc. 68 (1950), 6275.Google Scholar
Kaplansky, I., Infinite-dimensional quadratic forms permitting composition. Proc. Amer. Math. Soc. 4 (1953), 956–60. 360Google Scholar
Kaplansky, I., Ring isomorphisms of Banach algebras. Canad. J. Math. 6 (1954), 374–81. 596, 597Google Scholar
Kaplansky, I., ‘Problems in the theory of rings’ revisited. Amer. Math. Monthly 77 (1970), 445–54.Google Scholar
Kaup, W., Algebraic characterization of symmetric complex Banach manifolds. Math. Ann. 228 (1977), 3964. 2, 209, 210, 211, 241Google Scholar
Kaup, W., A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z. 183 (1983), 503–29. xix, 2, 209, 210, 211, 241Google Scholar
Kaup, W., Contractive projections on Jordan C -algebras and generalizations. Math. Scand. 54 (1984), 95100. xix, 207, 210Google Scholar
Kaup, W., On real Cartan factors. Manuscripta Math. 92 (1997), 191222. 460Google Scholar
Kaup, W., JB -triple. In [741], pp. 218–19. 462Google Scholar
Kaup, W. and Upmeier, H., Jordan algebras and symmetric Siegel domains in Banach spaces. Math. Z. 157 (1977), 179200. 211Google Scholar
Kawamura, K., On a conjecture of Wood. Glasgow Math. J. 47 (2005), 15.Google Scholar
Kelley, J. L. and Vaught, R. L., The positive cone in Banach algebras. Trans. Amer. Math. Soc. 74 (1953), 4455.Google Scholar
Kervaire, M., Non-parallelizability of the n sphere for n > 7. Proc. Nat. Acad. Sci. USA 44 (1958), 280–3.Google Scholar
Kleinecke, D. C., On operator commutators. Proc. Amer. Math. Soc. 8 (1957), 535–6.Google Scholar
Kleinfeld, E., Primitive alternative rings and semi-simplicity. Amer. J. Math. 77 (1955), 725–30. 570Google Scholar
Koliha, J. J., Isolated spectral points. Proc. Amer. Math. Soc. 124 (1996), 3417–24.Google Scholar
Koszmider, P., Martín, M., and Merí, J., Isometries on extremely non-complex Banach spaces. J. Inst. Math. Jussieu 10 (2011), 325–48.Google Scholar
Krupnik, N., Roch, S., and Silbermann, B., On C -algebras generated by idempotents. J. Funct. Anal. 137 (1996), 303–19.Google Scholar
Kulkarni, S. H., A very simple and elementary proof of a theorem of Ingelstam. Amer. Math. Monthly 111 (2004), 54–8.Google Scholar
Kunen, K. and Rosenthal, H., Martingale proofs of some geometrical results in Banach space theory. Pacific J. Math. 100 (1982), 153–75.Google Scholar
Kurosch, A., Ringtheoretische Probleme, die mit dem Burnsideschen Problem über periodische Gruppen in Zusammenhang stehen. Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 5 (1941), 233–40.Google Scholar
Kuwata, S., Born–Infeld Lagrangian using Cayley–Dickson algebras. Internat. J. Modern Physics A 19 (2004), 1525–48.Google Scholar
Laustsen, N. J., On ring-theoretic (in)finiteness of Banach algebras of operators on Banach spaces. Glasgow Math. J. 45 (2003), 1119.Google Scholar
Leung, C.-W., Ng, C.-K., and Wong, N.-C., Geometric unitaries in JB-algebras. J. Math. Anal. Appl. 360 (2009), 491–4.Google Scholar
Lima, Å., The metric approximation property, norm-one projections and intersection properties of balls. Israel J. Math. 84 (1993), 451–75.Google Scholar
Loos, O., Fitting decomposition in Jordan systems. J. Algebra 136 (1991), 92102.Google Scholar
Loos, O., Properly algebraic and spectrum-finite ideals in Jordan systems. Math. Proc. Cambridge Philos. Soc. 114 (1993), 149–61. 600Google Scholar
Loos, O., On the set of invertible elements in Banach Jordan algebras. Results Math. 29 (1996), 111–14. 597Google Scholar
Loos, O., Trace and norm for reduced elements of Jordan pairs. Comm. Algebra 25 (1997), 3011–42. 601Google Scholar
Loos, O., Nuclear elements in Banach Jordan pairs. In [705], pp. 111–17. 601Google Scholar
Loy, R. J., Maximal ideal spaces of Banach algebras of derivable elements. J. Austral. Math. Soc. 11 (1970), 310–12.Google Scholar
Lumer, G., Semi-inner-product spaces. Trans. Amer. Math. Soc. 100 (1961), 2943.Google Scholar
Lumer, G., Complex methods, and the estimation of operator norms and spectra from real numerical ranges. J. Funct. Anal. 10 (1972), 482–95.Google Scholar
Lumer, G. and Phillips, R. S., Dissipative operators in a Banach space. Pacific J. Math. 11 (1961), 679–98. 208Google Scholar
Macdonald, I. G., Jordan algebras with three generators. Proc. London Math. Soc. 10 (1960), 395408.Google Scholar
Magajna, B., Weak* continuous states on Banach algebras. J. Math. Anal. Appl. 350 (2009), 252–5.Google Scholar
Maouche, A., Caractérisations spectrales du radical et du socle d’une paire de Jordan–Banach. Canad. Math. Bull. 40 (1997), 488–97. 603Google Scholar
Maouche, A., Spectrum preserving linear mappings for scattered Jordan–Banach algebras. Proc. Amer. Math. Soc. 127 (1999), 3187–90. 603Google Scholar
Marcos, J. C., Rodríguez, A., and Velasco, M. V., A note on topological divisors of zero and division algebras. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 109 (2015), 93100.Google Scholar
Marcos, J. C. and Velasco, M. V., The Jacobson radical of a non-associative algebra and the uniqueness of the complete norm topology. Bull. London Math. Soc. 42 (2010), 1010–20.Google Scholar
Marcos, J. C. and Velasco, M. V., Continuity of homomorphisms into power-associative complete normed algebras. Forum Math. 25 (2013), 1109–25.Google Scholar
Martín, M., The group of isometries of a Banach space and duality. J. Funct. Anal. 255 (2008), 2966–76.Google Scholar
Martín, M. and Merí, J., Numerical index of some polyhedral norms on the plane. Linear Multilinear Algebra 55 (2007), 175–90.Google Scholar
Martín, M., Merí, J., and Payá, R., On the intrinsic and the spatial numerical range. J. Math. Anal. Appl. 318 (2006), 175–89.Google Scholar
Martín, M., Merí, J., and Rodríguez, A., Finite-dimensional Banach spaces with numerical index zero. Indiana Univ. Math. J. 53 (2004), 1279–89.Google Scholar
Martín, M. and Payá, R., Numerical index of vector-valued function spaces. Studia Math. 142 (2000), 269–80.Google Scholar
Martínez, J., JV-algebras. Math. Proc. Cambridge Philos. Soc. 87 (1980), 4750. 597Google Scholar
Martínez, J., Holomorphic functional calculus in Jordan–Banach algebras. In [749], pp. 125–34. 597Google Scholar
Martínez, J., Tracial elements for nonassociative H -algebras. In [733], pp. 257–68. xxv, 550Google Scholar
Martínez, J., Mena, J. F., Payá, R., and Rodríguez, A., An approach to numerical ranges without Banach algebra theory. Illinois J. Math. 29 (1985), 609–25. 673Google Scholar
Martínez, J. and Peralta, A. M., Separate weak-continuity of the triple product in dual real JB -triples. Math. Z. 234 (2000), 635–46. 243Google Scholar
Martínez, J. and Rodríguez, A., Imbedding elements whose numerical range has a vertex at zero in holomorphic semigroups. Proc. Edinburgh Math. Soc. 28 (1985), 91–5.Google Scholar
Mathieu, M., Rings of quotients of ultraprime Banach algebras, with applications to elementary operators. In [773], pp. 297–317. xxii, 408, 468, 547Google Scholar
Maurey, B., Banach spaces with few operators. In [757], pp. 1247–97.Google Scholar
Mazet, P., La preuve originale de S. Mazur pour son théorème sur les algèbres normées. Gaz. Math., Soc Math. Fr. 111 (2007), 511.Google Scholar
Mazur, S., Über konvexe Mengen in linearen normierten Räumen. Studia Math. 4 (1933), 7084.Google Scholar
Mazur, S., Sur les anneaux linéaires. C. R. Acad. Sci. Paris 207 (1938), 1025–7.Google Scholar
McCrimmon, K., Norms and noncommutative Jordan algebras. Pacific J. Math. 15 (1965), 925–56.Google Scholar
McCrimmon, K., Macdonald’s theorem with inverses. Pacific J. Math. 21 (1967), 315–25.Google Scholar
McCrimmon, K., The radical of a Jordan algebra. Proc. Nat. Acad. Sci. USA 62 (1969), 671–8. 597Google Scholar
McCrimmon, K., Noncommutative Jordan rings. Trans. Amer. Math. Soc. 158 (1971), 133. xxi, 273, 348, 411Google Scholar
McCrimmon, K. and Zel’manov, E., The structure of strongly prime quadratic Jordan algebras. Adv. Math. 69 (1988), 133222. xxi, 348, 365, 464Google Scholar
McGuigan, R., Strongly extreme points in Banach spaces. Manuscripta Math. 5 (1971), 113–22.Google Scholar
McIntosh, A., Functions and derivations of C -algebras. J. Funct. Anal. 30 (1978), 264–75.Google Scholar
Medbouhi, A. and Tajmouati, A., Calcul fonctionnel harmonique dans les algèbres de Banach alternatives involutives et applications. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), 141–52.Google Scholar
Mena, J. F. and Rodríguez, A., Weakly compact operators on non-complete normed spaces. Expo. Math. 27 (2009), 143–51.Google Scholar
Mena, J. F. and Rodríguez, A., Compact and weakly compact operators on non-complete normed spaces. In [704], pp. 205–11.Google Scholar
Meyberg, A., Identitäten und das Radikal in Jordan-Tripelsystemen. Math. Ann. 197 (1972), 203–20.Google Scholar
Milman, V. D., The infinite-dimensional geometry of the unit sphere of a Banach space. Soviet Math. Dokl. 8 (1967), 1440–4.Google Scholar
Milnor, J., Some consequences of a theorem of Bott. Ann. of Math. 68 (1958), 444–9.Google Scholar
Moore, R. T., Hermitian functionals on B-algebras and duality characterizations of C -algebras. Trans. Amer. Math. Soc. 162 (1971), 253–65.Google Scholar
Moreno, A., Distinguishing Jordan polynomials by means of a single Jordan-algebra norm. Studia Math. 122 (1997), 6773. xxii, 470Google Scholar
Moreno, A. and Rodríguez, A., On the Zel’manovian classification of prime JB -triples. J. Algebra 226 (2000), 577613. xxii, 422, 458, 460, 461Google Scholar
Moreno, A. and Rodríguez, A., On the Zel’manovian classification of prime JB - and JBW -triples. Comm. Algebra 31 (2003), 1301–28. xxii, 458, 459, 460, 461Google Scholar
Moreno, A. and Rodríguez, A., Introducing Analysis in Zel’manov’s theorems for Jordan systems. In Comptes Rendus de la Premièr Rencontre Maroco-Andalouse sur les Algèbres et leurs Applications, Tétouan, Septembre 2001, pp. 836, Université Abdelmalek Essaadi, Faculté des Sciences, Tétouan, 2003. 462Google Scholar
Moreno, A. and Rodríguez, A., A bilinear version of Holsztynski’s theorem on isometries of C(X)-spaces. Studia Math. 166 (2005), 8391.Google Scholar
Moreno, A. and Rodríguez, A., On multiplicatively closed subsets of normed algebras. J. Algebra 323 (2010), 1530–52. xxvi, 652, 653Google Scholar
Moreno, A. and Rodríguez, A., Topologically nilpotent normed algebras. J. Algebra 368 (2012), 126–68. xxvi, 652, 653, 654, 655, 656, 658Google Scholar
Moreno, G., The zero divisors of the Cayley–Dickson algebras over the real numbers. Bol. Soc. Mat. Mexicana 4 (1998), 1328.Google Scholar
Moreno, G., Alternative elements in the Cayley–Dickson algebras. In Topics in mathematical physics, general relativity and cosmology in honor of Jerzy Plebañski , pp. 333–46, World Sci. Publ., Hackensack, NJ, 2006.Google Scholar
Moutassim, A. and Rochdi, A., Sur les algèbres préhilbertiennes vérifiant ‖a 2‖ ≤‖a2 . Adv. appl. Clifford alg. 18 (2008), 269–78.Google Scholar
Nagumo, M., Einige analytishe Untersuchunger in linearen metrishen Ringen. Jap. J. Math. 13 (1936), 6180.Google Scholar
Nakamura, M., Complete continuities of linear operators. Proc. Japan Acad. 27 (1951), 544–7.Google Scholar
Navarro-Pascual, J. C. and Navarro, M. A., Unitary operators in real von Neumann algebras. J. Math. Anal. Appl. 386 (2012), 933–8.Google Scholar
Neher, E., Generators and relations for 3-graded Lie algebras, J. Algebra 155 (1993), 135. xxv, 554Google Scholar
von Neumann, J., On an algebraic generalization of the quantum mechanical formalism I. Mat. Sb. 1 (1936), 415–84.Google Scholar
Neumann, M. M., Rodríguez, A., and Velasco, M. V., Continuity of homomorphisms and derivations on algebras of vector-valued functions. Quart. J. Math. Oxford 50 (1999), 279300. 596, 709Google Scholar
Nieto, J. I., Normed right alternative algebras over the reals. Canad. J. Math. 24 (1972), 1183–6.Google Scholar
Nieto, J. I. Gateaux differentials in Banach algebras. Math. Z. 139 (1974), 2334.Google Scholar
Oja, E., On bounded approximation properties of Banach spaces. In Banach algebras 2009, pp. 219–31, Banach Center Publ. 91, Polish Acad. Sci. Inst. Math., Warsaw, 2010.Google Scholar
Okayasu, T., A structure theorem of automorphisms of von Neumann algebras. Tôhoku Math. J. 20 (1968), 199206.Google Scholar
Okubo, S., Pseudo-quaternion and pseudo-octonion algebras. Hadronic J. 1 (1978), 1250–78.Google Scholar
Okubo, S. and Osborn, J. M., Algebras with nondegenerate associative symmetric forms permitting composition. Comm. Algebra 9 (1981), 1233–61.Google Scholar
Olsen, C. L. and Pedersen, G. K., Convex combinations of unitary operators in von Neumann algebras. J. Funct. Anal. 66 (1986), 365–80.Google Scholar
Osborn, J. M., Quadratic division algebras. Trans. Amer. Math. Soc. 105 (1962), 202–21.Google Scholar
Osborn, J. M., Varieties of algebras. Adv. Math. 8 (1972), 163369.Google Scholar
Ostrowski, A., Über einige Lösungen der Funktionalgleichung Ψ(x)Ψ(y) = Ψ(xy). Acta Math. 41 (1918), 271–84.Google Scholar
Palais, R. S., The classification of real division algebras. Amer. Math. Monthly 75 (1968), 366–8.Google Scholar
Palmer, T. W., Characterizations of C -algebras. Bull. Amer. Math. Soc. 74 (1968), 538–40.Google Scholar
Palmer, T. W., Unbounded normal operators on Banach spaces. Trans. Amer. Math. Soc. 133 (1968), 385414.Google Scholar
Palmer, T. W., Characterizations of C -algebras II. Trans. Amer. Math. Soc. 148 (1970), 577–88.Google Scholar
Palmer, T. W., Real C -algebras. Pacific J. Math. 35 (1970), 195204.Google Scholar
Palmer, T. W., Spectral algebras. Rocky Mountain J. Math. 22 (1992), 293328.Google Scholar
Paterson, A. L. T., Isometries between B -algebras. Proc. Amer. Math. Soc. 22 (1969), 570–2.Google Scholar
Paterson, A. L. T. and Sinclair, A. M., Characterization of isometries between C -algebras. J. London Math. Soc. 5 (1972), 755–61.Google Scholar
Payá, R., Pérez, J., and Rodríguez, A., Non-commutative Jordan C -algebras. Manuscripta Math. 37 (1982), 87120. xx, xxi, 3, 19, 398, 411, 421Google Scholar
Payá, R., Pérez, J., and Rodríguez, A., Type I factor representations of non-commutative JB -algebras. Proc. London Math. Soc. 48 (1984), 428–44. xx, xxi, 398, 411, 421Google Scholar
Pedersen, G. K., Measure theory in C -algebras II. Math. Scand. 22 (1968), 6374.Google Scholar
Pedersen, G. K., The λ-function in operator algebras. J. Operator Theory 26 (1991), 345–81.Google Scholar
Peralta, A. M., On the axiomatic definition of real JB -triples. Math. Nachr. 256 (2003), 100–6.Google Scholar
Peralta, A. M., Positive definite hermitian mappings associated to tripotent elements. Expo. Math. 33 (2015), 252–8.Google Scholar
Peresi, L. A., Other nonassociative algebras. In The concise handbook of algebra (eds. Mikhalev, A. V. and Pilz, G. F.), pp. 343–7, Dordrecht, Kluwer Academic, 2002.Google Scholar
Pérez, J., Rico, L., and Rodríguez, A., Full subalgebras of Jordan–Banach algebras and algebra norms on JB -algebras. Proc. Amer. Math. Soc. 121 (1994), 1133–43. 336, 597Google Scholar
Pérez, J., Rico, L., Rodríguez, A., and Villena, A. R., Prime Jordan–Banach algebras with nonzero socle. Comm. Algebra 20 (1992), 1753. 598Google Scholar
Perlis, S., A characterization of the radical of an algebra. Bull. Amer. Math. Soc. 48 (1942), 128–32.Google Scholar
Phelps, R. R., Extreme points in function algebras. Duke Math. J. 32 (1965), 267–77.Google Scholar
Popa, S., On the Russo–Dye theorem. Michigan Math. J. 28 (1981), 311–15.Google Scholar
Pták, V., On the spectral radius in Banach algebras with involution. Bull. London Math. Soc. 2 (1970), 327–34.Google Scholar
Pták, V., Banach algebras with involution. Manuscripta Math. 6 (1972), 245–90.Google Scholar
Putter, P. S. and Yood, B., Banach Jordan ∗-algebras. Proc. London Math. Soc. 41 (1980), 2144. 597Google Scholar
Raeburn, I. and Sinclair, A. M., The C -algebra generated by two projections. Math. Scand. 65 (1989), 278–90.Google Scholar
Raffin, R., Anneaux a puissances commutatives and anneaux flexibles. C. R. Acad. Sci. Paris 230 (1950), 804–6.Google Scholar
Rambla, F., A counterexample to Wood’s conjecture. J. Math. Anal. Appl. 317 (2006), 659–67.Google Scholar
Ransford, T. J., A short proof of Johnson’s uniqueness-of-norm theorem. Bull. London Math. Soc. 21 (1989), 487–8.Google Scholar
Rickart, C. E., The singular elements of a Banach algebra. Duke Math. J. 14 (1947), 1063–77.Google Scholar
Rickart, C. E., The uniqueness of norm problem in Banach algebras. Ann. of Math. 51 (1950), 615–28.Google Scholar
Rickart, C. E., On spectral permanence for certain Banach algebras. Proc. Amer. Math. Soc. 4 (1953), 191–6.Google Scholar
Rickart, C. E., An elementary proof of a fundamental theorem in the theory of Banach algebras. Michigan Math. J. 5 (1958), 75–8.Google Scholar
Riesz, F., Sur certains systèmes singuliers d’équations intégrales. Ann. Sci. École Norm. Sup. 28 (1911), 3362.Google Scholar
Riesz, F., Über lineare Funktionalgleichungen. Acta Math. 41 (1916), 7198.Google Scholar
Robertson, A. G., A note on the unit ball in C -algebras. Bull. London Math. Soc. 6 (1974), 333–5.Google Scholar
Robertson, A. G. and Youngson, M. A., Positive projections with contractive complements on Jordan algebras. J. London Math. Soc. 25 (1982), 365–74. 210Google Scholar
Rochdi, A., Eight-dimensional real absolute valued algebras with left unit whose automorphism group is trivial. Int. J. Math. Math. Sci. 70 (2003), 4447–54.Google Scholar
Rochdi, A. and Rodríguez, A., Absolute valued algebras with involution. Comm. Algebra 37 (2009), 1151–9.Google Scholar
Rodríguez, A., Algebras estelares de Banach con elemento unidad. In Actas de las I Jornadas Matemáticas Hispano-Lusitanas, pp. 189210, Madrid, 1973.Google Scholar
Rodríguez, A., Derivaciones en álgebras normadas y commutatividad. Cuadernos del Dpto. de Estadística Matemática (Granada) 2 (1975), 5168.Google Scholar
Rodríguez, A., Teorema de estructura de los Jordan-isomorfismos de las C -álgebras. Rev. Mat. Hispano-Americana 37 (1977), 114–28.Google Scholar
Rodríguez, A., Rango numérico y derivaciones cerradas de las álgebras de Banach. In V Jornadas luso-espanholas de matemáticas, pp. 179200, Aveiro, 1978.Google Scholar
Rodríguez, A., A Vidav–Palmer theorem for Jordan C -algebras and related topics. J. London Math. Soc. 22 (1980), 318–32.Google Scholar
Rodríguez, A., Non-associative normed algebras spanned by hermitian elements. Proc. London Math. Soc. 47 (1983), 258–74. 210Google Scholar
Rodríguez, A., The uniqueness of the complete algebra norm topology in complete normed nonassociative algebras. J. Funct. Anal. 60 (1985), 115. 548, 597Google Scholar
Rodríguez, A., Mutations of C -algebras and quasiassociative JB -algebras. Collectanea Math. 38 (1987), 131–5.Google Scholar
Rodríguez, A., Jordan axioms for C -algebras. Manuscripta Math. 61 (1988), 279314. xxiv, 474, 549Google Scholar
Rodríguez, A., Automatic continuity with application to C -algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 345–7.Google Scholar
Rodríguez, A., An approach to Jordan–Banach algebras from the theory of nonassociative complete normed algebras. In [749], pp. 1–57. 584, 585, 586Google Scholar
Rodríguez, A., One-sided division absolute valued algebras. Publ. Mat. 36 (1992), 925–54.Google Scholar
Rodríguez, A., Closed derivations of Banach algebras. In Homenaje a Pablo Bobillo Guerrero, pp. 21–8, Univ. Granada, Granada, 1992.Google Scholar
Rodríguez, A., Primitive nonassociative normed algebras and extended centroid. In [734], pp. 233–43. 408, 601, 602Google Scholar
Rodríguez, A., Absolute valued algebras of degree two. In [733], pp. 350–6.Google Scholar
Rodríguez, A., Jordan structures in Analysis. In [764], pp. 97–186. xxii, 338, 340, 408, 462, 467, 549, 550, 553, 597, 601Google Scholar
Rodríguez, A., Continuity of densely valued homomorphisms into H -algebras. Quart . J. Math. Oxford 46 (1995), 107–18. xxiv, 546, 548, 549Google Scholar
Rodríguez, A., Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces. In Encuentro de Análisis Matemático, Homenaje al profesor B. Rodríguez-Salinas (eds. Bombal, F., Hernández, F. L., Jiménez y, P. de María, J. L.), Rev. Mat. Univ. Complutense Madrid 9 (1996), 149–89.Google Scholar
Rodríguez, A., Isometries and Jordan isomorphisms onto C -algebras. J. Operator Theory 40 (1998), 7185. 274, 346Google Scholar
Rodríguez, A., Continuity of homomorphisms into normed algebras without topological divisors of zero. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 94 (2000), 505–14. xxv, 595Google Scholar
Rodríguez, A., Sobre el tamaño de los conjuntos de números. In Actas del Encuentro de Matemáticos Andaluces, Sevilla 2000, Volumen I, pp. 235–48, Secretariado de Publicaciones de la Universidad de Sevilla, Sevilla, 2001.Google Scholar
Rodríguez, A., A numerical range characterization of uniformly smooth Banach spaces. Proc. Amer. Math. Soc. 129 (2001), 815–21.Google Scholar
Rodríguez, A., Banach–Jordan algebra. In [741], pp. 55–7. 462Google Scholar
Rodríguez, A., Absolute-valued algebras, and absolute-valuable Banach spaces. In Advanced Courses of Mathematical Analysis I, Proceedings of the First International School Cádiz, Spain 22–27 September 2002 (eds. Aizpuru-Tomás, A. and León-Saavedra, F.), pp. 99155, World Scientific, 2004.Google Scholar
Rodríguez, A., Numerical ranges of uniformly continuous functions on the unit sphere of a Banach space. J. Math. Anal. Appl. 297 (2004), 472–6. 208Google Scholar
Rodríguez, A., On Urbanik’s axioms for absolute valued algebras with involution. Comm. Algebra 36 (2008), 2588–92.Google Scholar
Rodríguez, A., Banach space characterizations of unitaries: a survey. J. Math. Anal. Appl. 369 (2010), 168–78.Google Scholar
Rodríguez, A., Approximately norm-unital products on C -algebras, and a nonassociative Gelfand–Naimark theorem. J. Algebra 347 (2011), 224–46. 421Google Scholar
Rodríguez, A., Slinko, A. M., and Zel’manov, E. I., Extending the norm from Jordan– Banach algebras of hermitian elements to their associative envelopes. Comm. Algebra 22 (1994), 1435–55. xxii, xxiii, 437, 470, 471, 472Google Scholar
Rodríguez, A. and Velasco, M. V., Continuity of homomorphisms and derivations on Banach algebras with an involution. In Function Spaces; Proceedings of the Third Conference on Function Spaces, May 19–23, 1998, Southern Illinois University at Edwardsville (ed. Jarosz, K.), pp. 289–98, Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999. xxii, 474, 475Google Scholar
Rodríguez, A. and Velasco, M. V., A non-associative Rickart’s dense-range-homomorphism theorem. Quart. J. Math. Oxford 54 (2003), 367–76. 597Google Scholar
Rordam, M., Advances in the theory of unitary rank and regular approximation. Ann. of Math. 128 (1988), 153–72.Google Scholar
Rosenthal, H., The Lie algebra of a Banach space. In Banach Spaces, pp. 129–57, Lecture Notes in Math. 1166, 1985.Google Scholar
Rosenthal, H., Functional Hilbertian sums. Pacific J. Math. 124 (1986), 417–67.Google Scholar
Rota, G.-C. and Strang, W. G., A note on the joint spectral radius. Indag. Math. 22 (1960), 379–81. xxvi, 650Google Scholar
Rowen, L. H., A short proof of the Chevalley–Jacobson density theorem, and a generalization. Amer. Math. Monthly 85 (1978), 185–6.Google Scholar
Ruan, Z.-J., Subspaces of C*-algebras. J. Funct. Anal. 76 (1988), 217–30.Google Scholar
Russo, B., Structure of JB -triples. In [764], pp. 209–80.Google Scholar
Russo, B. and Dye, H. A., A note on unitary operators in C -algebras. Duke Math. J. 33 (1966), 413–16.Google Scholar
Sakai, S., On a conjecture of Kaplansky. Tôhoku Math. J. 12 (1960), 31–3.Google Scholar
Sasiada, E. and Cohn, P. M., An example of a simple radical ring. J. Algebra 5 (1967), 373–7. 659Google Scholar
Schafer, R. D., On the algebras formed by the Cayley–Dickson process. Amer. J. Math. 76 (1954), 435–46.Google Scholar
Schafer, R. D., Noncommutative Jordan algebras of characteristic 0. Proc. Amer. Math. Soc. 6 (1955), 472–5.Google Scholar
Schafer, R. D., Generalized standard algebras. J. Algebra 12 (1969), 386417. 657Google Scholar
Schatz, J. A., Review of [273]. Math. Rev. 14 (1953), 884.Google Scholar
Schauder, J., Über lineare, vollstetige Funktionaloperationen. Studia Math. 2 (1930), 183–96.Google Scholar
Schoenberg, I. J., A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal. Proc. Amer. Math. Soc. 3 (1952), 961–4.Google Scholar
Schue, J. R., Hilbert space methods in the theory of Lie algebras, Trans. Amer. Math. Soc. 95 (1960), 6980. 553, 554Google Scholar
Schue, J. R., Cartan decompositions for L -algebras. Trans. Amer. Math. Soc. 98 (1961), 334–49. 553Google Scholar
Schur, 1. I., Neue Begründung der Theorie der Gruppencharaktere. Sitzungsberichte der Preuβischen Akademie der Wissenschaften 1905 Physik-Math. Klasse 406–32. Reprinted in Gesammelte Abhandlungen Vol. I pp. 143–69, Spriger, Berlin, 1973.Google Scholar
Segal, I. E., Irreducible representations of operator algebras. Bull. Amer. Math. Soc. 53 (1947), 7388.Google Scholar
Segre, B., La teoria delle algebre ed alcune questione di realtà. Univ. Roma, Ist. Naz. Alta. Mat., Rend. Mat. e Appl., serie 5 13 (1954), 157–88.Google Scholar
Shelah, S. and Steprans, J., A Banach space on which there are few operators. Proc. Amer. Math. Soc. 104 (1988), 101–5.Google Scholar
Sherman, D., A new proof of the noncommutative Banach–Stone theorem. Quantum probability , 363–75, Banach Center Publ. 73, Polish Acad. Sci. Inst. Math., Warsaw, 2006.Google Scholar
Shilov, G., On the extension of maximal ideals. C. R. (Doklady) Acad. Sci. URSS 29 (1940), 83–4.Google Scholar
Shirali, S. and Ford, J. W. M., Symmetry in complex involutory Banach algebras. II. Duke Math. J. 37 (1970), 275–80.Google Scholar
Shirokov, F. V., Proof of a conjecture by Kaplansky. (In Russian.) Uspekhi Mat. Nauk 11 (1956) 167–8.Google Scholar
Shirshov, A. I., On special J-rings. (In Russian.) Mat. Sb. 38 (80) (1956), 149–66.Google Scholar
Shirshov, A. I., On some non-associative nil-rings and algebraic algebras. Mat. Sb. 41 (83) (1957), 381–94.Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Joint spectral radius, operator semigroups, and a problem of W. Wojtynski. J. Funct. Anal. 177 (2000), 383441. xxvi, 652, 653, 654, 656Google Scholar
Shultz, F. W., On normed Jordan algebras which are Banach dual spaces. J. Funct. Anal. 31 (1979), 360–76. 19, 398, 401Google Scholar
Siddiqui, A. A., Self-adjointness in unitary isotopes of JB -algebras. Arch. Math. 87 (2006), 350–8.Google Scholar
Siddiqui, A. A., Asymmetric decompositions of vectors in JB -algebras. Arch. Math. (Brno) 42 (2006), 159–66.Google Scholar
Siddiqui, A. A., JB -algebras of topological stable rank 1. Int. J. Math. Math. Sci. 2007, Art. ID 37186, 24 pp.Google Scholar
Siddiqui, A. A., A proof of the Russo–Dye theorem for JB -algebras. New York J. Math. 16 (2010), 5360.Google Scholar
Siddiqui, A. A., Convex combinations of unitaries in JB -algebras. New York J. Math. 17 (2011), 127–37.Google Scholar
Siddiqui, A. A., The λ u -function in JB -algebras. New York J. Math. 17 (2011), 139–47.Google Scholar
Sinclair, A. M., Jordan automorphisms on a semisimple Banach algebra. Proc. Amer. Math. Soc. 25 (1970), 526–8.Google Scholar
Sinclair, A. M., Jordan homomorphisms and derivations on semisimple Banach algebras. Proc. Amer. Math. Soc. 24 (1970), 209–14.Google Scholar
Sinclair, A. M., The states of a Banach algebra generate the dual. Proc. Edinburgh Math. Soc. 17 (1970/71), 341–4.Google Scholar
Sinclair, A. M., The norm of a hermitian element in a Banach algebra. Proc. Amer. Math. Soc. 28 (1971), 446–50.Google Scholar
Sinclair, A. M., The Banach algebra generated by a derivation. In Spectral theory of linear operators and related topics (Timisoara/Herculane, 1983), pp. 241–50, Oper. Theory Adv. Appl. 14, Birkhäuser, Basel, 1984.Google Scholar
Singer, I. M. and Wermer, J., Derivations on commutative normed algebras. Math. Ann. 129 (1955), 260–4.Google Scholar
Skorik, A. and Zaidenberg, M., On isometric reflexions in Banach spaces. Math. Physics, Analysis, Geometry 4 (1997), 212–47.Google Scholar
Skosyrskii, V. G., Strongly prime noncommutative Jordan algebras. (In Russian.) Trudy Inst. Mat. (Novosibirk) 16 (1989), 131–64, Issled. po Teor. Kolets i Algebr, 198–9. 411, 422Google Scholar
Skosyrskii, V. G., Primitive Jordan algebras. Algebra Logic 31 (1993), 110–20. xxii, 462Google Scholar
Slinko, A. M., Complete metric Jordan algebras. Mat. Zametki 447 (1990), 100–5. English translation: Math. Notes 47 (1990), 491–4. 597Google Scholar
Slinko, A. M., 1, 2, 4, 8, … What comes next? Extracta Math. 19 (2004), 155–61.Google Scholar
Smiley, M. F., The radical of an alternative ring. Ann. of Math. 49 (1948), 702–9.Google Scholar
Smiley, M. F., Right H -algebras. Proc. Amer. Math. Soc. 4 (1953), 14.Google Scholar
Smiley, M. F., Real Hilbert algebras with identity. Proc. Amer. Math. Soc. 16 (1965) 440–1.Google Scholar
Smith, R. R., On Banach algebra elements of thin numerical range. Math. Proc. Cambridge Philos. Soc. 86 (1979), 7183.Google Scholar
Smith, R. R., The numerical range in the second dual of a Banach algebra. Math. Proc. Cambridge Philos. Soc. 89 (1981), 301–7.Google Scholar
Šmulyan, V., Sur la structure de la sphère unitaire dans l’espace de Banach. Math. Sb. 9 (1941), 545–61.Google Scholar
Spatz, I. N., Smooth Banach algebras. Proc. Amer. Math. Soc. 22 (1969), 328–9.Google Scholar
Spitkovsky, I., Once more on algebras generated by two projections. Linear Algebra Appl. 208 / 209 (1994), 377–95.Google Scholar
Spurný, J., A note on compact operators on normed linear spaces. Expo. Math. 25 (2007), 261–3.Google Scholar
Stachó, L. L., A projection principle concerning biholomorphic automorphisms. Acta Sci. Math. (Szeged) 44 (1982), 99124. xix, 207, 210Google Scholar
Steen, S. W. P., Introduction to the theory of operators. V. Metric rings, Proc. Cambridge Philos. Soc. 36 (1940), 139–49. 550Google Scholar
Stinespring, W. F., Positive functions on C -algebras. Proc. Amer. Math. Soc. 6, (1955), 211–16.Google Scholar
Stone, M. H., Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41 (1937), 375481.Google Scholar
Størmer, E., On the Jordan structure of C -algebras. Trans. Amer. Math. Soc. 120 (1965), 438–47.Google Scholar
Størmer, E., Jordan algebras of type I. Acta Math. 115 (1966), 165–84. 339Google Scholar
Størmer, E., Irreducible Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc. 130 (1968), 153–66. 339Google Scholar
Strasek, R. and Zalar, B., Uniform primeness of classical Banach Lie algebras of compact operators. Publ. Math. Debrecen 61 (2002), 325–40.Google Scholar
Strzelecki, E., Metric properties of normed algebras. Studia Math. 23 (1963), 4151.Google Scholar
Strzelecki, E., Power-associative regular real normed algebras. J. Austral. Math. Soc. 6 (1966), 193209.Google Scholar
Suttles, D., A counterexample to a conjecture of Albert. Notices Amer. Math. Soc., 19 (1972), A-566.Google Scholar
Szankowski, A., B(H) does not have the approximation property. Acta Math. 147 (1981), 89108.Google Scholar
Talponen, J., A note on the class of superreflexive almost transitive Banach spaces. Extracta Math. 23 (2008), 16.Google Scholar
Terekhin, P. A., Trigonometric algebras. J. Math. Sci. (New York) 95 (1999), 2156–60.Google Scholar
Thomas, M. P., The image of a derivation is contained in the radical. Ann. of Math. 128 (1988), 435–60.Google Scholar
Thomas, M. P., Primitive ideals and derivations on noncommutative Banach algebras. Pacific J. Math. 159 (1993), 139–52.Google Scholar
Toeplitz, O., Das algebraische Analogon zu einem Satze von Fejer. Math. Z. 2 (1918), 187–97.Google Scholar
Topping, D. M., An isomorphism invariant for spin factors. J. Math. Mech. 15 (1966), 1055–63.Google Scholar
Turovskii, Yu. V., On spectral properties of Lie subalgebras and on the spectral radius of subsets of a Banach algebra. (In Russian.) Spectral theory of operators and its applications, 6 (1985), 144–81. xxvi, 651Google Scholar
Uchiyama, M., Operator monotone functions which are defined implicitly and operator inequalities. J. Funct. Anal. 175 (2000), 330–47.Google Scholar
Urbanik, K., Absolute valued algebras with an involution. Fundamenta Math. 49 (1961), 247–58.Google Scholar
Urbanik, K., Remarks on ordered absolute valued algebras. Colloq. Math. 11 (1963), 31–9.Google Scholar
Urbanik, K. and Wright, F. B., Absolute valued algebras. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 285–6.Google Scholar
Urbanik, K. and Wright, F. B., Absolute valued algebras. Proc. Amer. Math. Soc. 11 (1960), 861–6.Google Scholar
Velasco, M. V., Spectral theory for non-associative complete normed algebras and automatic continuity. J. Math. Anal. Appl. 351 (2009), 97106.Google Scholar
Vesentini, E., On the subharmonicity of the spectral radius. Boll. Un. Mat. Ital. 1 (1968), 427–9.Google Scholar
Vidav, I., Eine metrische Kennzeichnung der selbstadjungierten Operatoren. Math. Z. 66 (1956), 121–8.Google Scholar
Villena, A. R., Continuity of derivations on H -algebras. Proc. Amer. Math. Soc. 122 (1994), 821–6. xxiv, 548, 549Google Scholar
Villena, A. R., Derivations on Jordan–Banach algebras. Studia Math. 118 (1996), 205–29. 466, 548Google Scholar
Villena, A. R., Automatic continuity in associative and nonassociative context. Irish Math. Soc. Bulletin 46 (2001), 4376.Google Scholar
Villena, A. R., Epimorphisms onto derivation algebras. Proc. Edinburgh Math. Soc. 46 (2003), 379–82.Google Scholar
Viola Devapakkiam, C., Jordan algebras with continuous inverse. Math. Japon. 16 (1971), 115–25. 597Google Scholar
Vowden, B. J., On the Gelfand–Neumark theorem. J. London Math. Soc. 42 (1967), 725–31.Google Scholar
Walsh, B., Classroom notes: The scarcity of cross products on Euclidean spaces. Amer. Math. Monthly 74 (1967), 188–94.Google Scholar
Wark, H. M., A non-separable reflexive Banach space on which there are few operators. J. London Math. Soc. 64 (2001), 675–89.Google Scholar
Wichmann, J., Hermitian ∗-algebras which are not symmetric. J. London Math. Soc. 8 (1974), 109–12.Google Scholar
Wichmann, J., On commutative B -equivalent algebras. Notices Amer. Math. Soc. (1975), Abstract 720–46–19.Google Scholar
Wichmann, J., The symmetric radical of an algebra with involution. Arch. Math. (Basel) 30 (1978), 83–8.Google Scholar
Wilansky, A., Letter to the Editor. Amer. Math. Monthly 91 (1984), 531.Google Scholar
Wilkins, T. J. D., Inessential ideals in Jordan–Banach algebras. Bull. London Math. Soc. 29 (1997), 7381. 603Google Scholar
Wojtaszczyk, P., Some remarks on the Daugavet equation. Proc. Amer. Math. Soc. 115 (1992), 1047–52.Google Scholar
Wood, G. V., Maximal symmetry in Banach spaces. Proc. Royal Irish Acad. 82A (1982), 177–86.Google Scholar
Wood, G. V., Maximal algebra norms. In Trends in Banach spaces and operator theory (Memphis, TN, 2001), pp. 335–45, Contemp. Math. 321, Amer. Math. Soc., Providence, RI, 2003.Google Scholar
Wright, F. B., Absolute valued algebras. Proc. Nat. Acad. Sci. USA 39 (1953), 330–2.Google Scholar
Wright, J. D. M., Jordan C -algebras. Michigan Math. J. 24 (1977), 291302. xx, 347, 398, 401Google Scholar
Wright, J. D. M. and Youngson, M. A., A Russo Dye theorem for Jordan C -algebras. In Functional analysis: surveys and recent results (Proc. Conf., Paderborn, 1976) (eds. Bierstedt, K. D. and Fuchssteiner, F.), pp. 279–82, North-Holland Math. Stud. 27, North-Holland, Amsterdam, 1977.Google Scholar
Wright, J. D. M. and Youngson, M. A., On isometries of Jordan algebras. J. London Math. Soc. 17 (1978), 339–44.Google Scholar
Wu, W., Locally pre-C -equivalent algebras. Proc. Amer. Math. Soc. 131 (2003), 555–62.Google Scholar
Yood, B., Topological properties of homomorphisms between Banach algebras. Amer. J. Math. 76 (1954), 155–67.Google Scholar
Yood, B., Homomorphisms on normed algebras. Pacific J. Math. 8 (1958), 373–81.Google Scholar
Yood, B., Faithful ∗-representations of normed algebras. Pacific J. Math. 10 (1960), 345–63.Google Scholar
Yood, B., Ideals in topological rings. Canad. J. Math. 16 (1964), 2845.Google Scholar
Yood, B., On axioms for B -algebras. Bull. Amer. Math. Soc. 76 (1970), 80–2.Google Scholar
Yost, D., A base norm space whose cone is not 1-generating. Glasgow Math. J. 25 (1984), 35–6. 690Google Scholar
Yost, D., Review of [650]. Zbl. Mat. 0544.46014.Google Scholar
Youngson, M. A., A Vidav theorem for Banach Jordan algebras. Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–72.Google Scholar
Youngson, M. A., Equivalent norms on Banach Jordan algebras. Math. Proc. Cambridge Philos. Soc. 86 (1979), 261–9. 597Google Scholar
Youngson, M. A., Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. 22 (1979), 93104.Google Scholar
Youngson, M. A., Nonunital Banach Jordan algebras and C -triple systems. Proc. Edinburgh Math. Soc. 24 (1981), 1929. 210Google Scholar
Zalar, B., Inner product characterizations of classical Cayley–Dickson algebras. In [733], pp. 405–9.Google Scholar
Zalar, B., On Hilbert spaces with unital multiplication. Proc. Amer. Math. Soc. 123 (1995), 1497–501.Google Scholar
Zalduendo, I., A simple example of a noncommutative Arens product. Publ. Mat. 35 (1991), 475–7.Google Scholar
Zelazko, W., On generalized topological divisors of zero in real m-convex algebras. Studia Math. 28 (1966/1967), 241–4.Google Scholar
Zeller-Meier, G., Sur les automorphismes des algèbres de Banach. C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A1131–2.Google Scholar
Zel’manov, E. I., Absolute zero-divisors and algebraic Jordan algebras. Siberian Math. J. 23 (1982), 841–54. 600Google Scholar
Zel’manov, E. I., On prime Jordan algebras II. Siberian Math. J. 24 (1983), 89104. xxi, 348, 364, 365, 366, 367, 401, 437Google Scholar
Zel’manov, E. I., On prime Jordan triple systems III. Siberian Math. J. 26 (1985), 7182. xxii, 421, 437, 438, 459, 461Google Scholar
Zemánek, J., A note on the radical of a Banach algebra. Manuscripta Math. 20 (1977), 191–6.Google Scholar
Zettl, H., A characterization of ternary rings of operators. Adv. Math. 48 (1983), 117–43. 459Google Scholar
Zhevlakov, K. A., Solvability of alternative nil-rings. Sibirsk. Mat. Z. 3 (1962), 368–77.Google Scholar
Zhevlakov, K. A., Coincidence of Smiley and Kleinfeld radicals in alternative rings. Algebra Logic 8 (1969), 175–81.Google Scholar
Zorn, M., Theorie der alternativen Ringe. Abh. Math. Sem. Univ. Hamburg 8 (1930), 123–47.Google Scholar
Zorn, M., Alternativkörper und quadratische Systeme. Abh. Math. Sem. Univ. Hamburg 9 (1933), 395402.Google Scholar
Albert, A. A., Structure of algebras. Revised printing, Amer. Math. Soc. Colloq. Publ. 24, American Mathematical Society, Providence, RI, 1961.Google Scholar
Albiac, F. and Kalton, N. J., Topics in Banach space theory . Grad. Texts in Math. 233, Springer, New York, 2006. 213, 236Google Scholar
Alfsen, E. M. and Shultz, F. W., Non-commutative spectral theory for affine function spaces on convex sets . Mem. Amer. Math. Soc. 6 (1976), no. 172.Google Scholar
Alfsen, E. M. and Shultz, F. W., Geometry of state spaces of operator algebras. Mathematics: Theory and Applications. Birkhäuser Boston, Inc., Boston, MA, 2003. 331, 411Google Scholar
Aliprantis, C. D. and Border, K. C., Infinite dimensional analysis. A hitchhiker’s guide. Third edition. Springer, Berlin, 2006.Google Scholar
Allan, G. R., Introduction to Banach spaces and algebras. Prepared for publication and with a preface by H. Garth Dales. Oxf. Grad. Texts Math. 20, Oxford University Press, Oxford, 2011.Google Scholar
Amir, D., Characterizations of inner product spaces. Oper. Theory Adv. Appl. 20, Birkhäuser Verlag, Basel–Boston–Stuttgart, 1986.Google Scholar
Andrunakievich, V. A. and Rjabuhin, Yu. M., Radicals of algebras and structural theory. (In Russian.) Contemporary Algebra ‘Nauka’, Moscow, 1979. 633 Google Scholar
Ara, P. and Mathieu, M., Local multipliers of C-algebras. Springer Monogr. Math., Springer, London, 2003. 401, 408, 550Google Scholar
Argyros, S. A. and Tolias, A., Methods in the theory of hereditarily indecomposable Banach spaces . Mem. Amer. Math. Soc. 170 (2004), no. 806.Google Scholar
Ash, R. B. and Novinger, W. P., Complex variables. Dover Publications, 2007.Google Scholar
Asimow, L. and Ellis, A. J., Convexity theory and its applications in functional analysis. London Math. Soc. Monogr. 16, Academic Press, London, 1980.Google Scholar
Aupetit, B., Propriétés spectrales des algèbres de Banach. Lecture Notes in Math. 735, Springer, Berlin, 1979. 401, 436, 498, 596, 597Google Scholar
Aupetit, B., A primer on spectral theory. Universitext, Springer, New York, 1991. 597, 599Google Scholar
Ayupov, S., Rakhimov, A., and Usmanov, S., Jordan, real and Lie structures in operator algebras . Math. Appl. 418, Kluwer Academic Publishers Group, Dordrecht, 1997.Google Scholar
Banach, S., Theory of linear operations. Translated from the French by F. Jellett. With comments by A. Pełczyński and Cz. Bessaga. North-Holland Math. Library 38, North-Holland Publishing Co., Amsterdam, 1987.Google Scholar
Beidar, K. I., Martindale, W. S. III, and Mikhalev, A. V., Rings with generalized identities . Monographs Textbooks Pure Appl. Math. 196, Marcel Dekker, New York, 1996. 401, 602Google Scholar
Beltita, D., Smooth homogeneous structures in operator theory. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 137, Chapman & Hall/CRC, Boca Raton, FL, 2006. xxiv, xxv, 154, 155, 174, 549, 554Google Scholar
Beltita, D. and Sabac, M., Lie algebras of bounded operators . Oper. Theory Adv. Appl. 120, Birkhäuser Verlag, Basel, 2001.Google Scholar
Berberian, S. K., Lectures in functional analysis and operator theory. Grad. Texts in Math. 15, Springer, New York–Heidelberg, 1974. 157, 183, 539Google Scholar
Blecher, D. P. and Merdy, Ch. Le, Operator algebras and their modules – an operator space approach. London Math. Soc. Monogr. New Series 30, Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford, 2004.Google Scholar
Block, R. E., Jacobson, N., Osborn, J. M., Saltman, D. J., and Zelinsky, D. (eds.), Adrian Albert, A., Collected mathematical papers: Associative algebras and Riemann matrices, Part 1. Amer. Math. Soc., Providence, RI, 1993. 664, 678Google Scholar
Block, R. E., Jacobson, N., Osborn, J. M., Saltman, D. J., and Zelinsky, D. (eds.), Adrian Albert, A., Collected mathematical papers: Nonassociative algebras and miscellany, Part 2. Amer. Math. Soc., Providence, RI, 1993. 664, 699Google Scholar
Boas, R. P., Entire functions. Academic Press Inc., New York, 1954.Google Scholar
Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras. London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, Cambridge, 1971.Google Scholar
Bonsall, F. F. and Duncan, J., Numerical ranges II. London Math. Soc. Lecture Note Ser. 10, Cambridge University Press, Cambridge, 1973.Google Scholar
Bonsall, F. F. and Duncan, J., Complete normed algebras. Ergeb. Math. Grenzgeb. 80, Springer, Berlin, 1973. xvii, 436, 545, 551, 584, 659Google Scholar
Bourbaki, N., Éléments de mathématique. Fasc. XXXII. Théories spectrales. Chapitre I: Algèbres normées. Chapitre II: Groupes localement compacts commutatifs . Actualités Scientifiques et Industrielles 1332, Hermann, Paris, 1967.Google Scholar
Bratteli, O., Derivations, dissipations and group actions on C-algebras . Lecture Notes in Math. 1229, Springer, Berlin, 1986.Google Scholar
Bratteli, O. and Robinson, D. W., Operator algebras and quantum statistical mechanics II . Texts Monographs Phys., Springer, New York, 1981.Google Scholar
Braun, H. and Koecher, M., Jordan-Algebren. Grundlehren Math. Wiss. 128, Springer, Berlin–New York, 1966.Google Scholar
Brelot, M., On topologies and boundaries in potential theory. (Enlarged edition of a course of lectures delivered in 1966). Lecture Notes in Math. 175, Springer, Berlin–New York, 1971.Google Scholar
Brešar, M., Chebotar, M. A., and Martindale, W. S. III, Functional identities. Front. Math., Birkhäuser Verlag, Basel, 2007. 602 Google Scholar
Caradus, S. R., Pfaffenberger, W. E., and Yood, B., Calkin algebras and algebras of operators on Banach spaces. Lecture Notes in Pure and Appl. Math. 9, Marcel Dekker Inc., New York, 1974.Google Scholar
Carmona, J., Morales, A., Peralta, A. M., and Ramírez, M. I. (eds.), Proceedings of Jordan structures in algebra and analysis meeting. Tribute to El Amin Kaidi for his 60th birthday. Almería 2009. Editorial Círculo Rojo, Almería 2010. 669, 674, 682Google Scholar
Castellón, A., Cuenca, J. A., Fernández, A., and Martín, C. (eds.), Proceedings of the International Conference on Jordan Structures (Málaga, 1997). Univ. Málaga, Málaga, 1999. 679, 680, 700, 707Google Scholar
Cerdà, J., Linear functional analysis. Grad. Stud. Math. 116, American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, 2010.Google Scholar
Chae, S. B., Holomorphy and calculus in normed spaces. With an appendix by Angus E. Taylor. Monographs Textbooks Pure Appl. Math. 92. Marcel Dekker Inc., New York, 1985. 23, 53Google Scholar
Chandid, A., Algèbres absolument valuées qui satisfont à (x p , x q , x r ) = 0. PhD thesis, Casablanca 2009.Google Scholar
Choquet, G., Cours d’analyse. Tome II: Topologie. Masson et Cie, Editeurs, Paris, 1964.Google Scholar
Chu, C.-H., Jordan structures in geometry and analysis. Cambridge Tracts in Math. 190, Cambridge University Press, New York, 2012. xix, 174, 207, 209, 210, 597, 711Google Scholar
Conway, J. B., A course in functional analysis. Second edition. Grad. Texts in Math. 96, Springer, New York, 1990.Google Scholar
Conway, J. H. and Smith, D. A., On quaternions and octonions: their geometry, arithmetic, and symmetry. A K Peters, Ltd., Natick, MA, 2003.Google Scholar
Cowie, E. R., Isometries in Banach algebras. PhD thesis, Swansea 1981.Google Scholar
Cuenca, J. A., Sobre H∗-álgebras no asociativas. Teoría de estructura de las H∗-álgebras de Jordan no conmutativas semisimples . PhD thesis, Granada 1982, Secretariado de Publicaciones de la Universidad de Málaga, 1984. xxiii, 545, 548, 597Google Scholar
Dales, H. G., Banach algebras and automatic continuity. London Math. Soc. Monogr. New Series 24, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 2000. 267, 414Google Scholar
Day, M. M., Normed linear spaces. Ergeb. Math. Grenzgeb. 21, Springer, Berlin, 1973.Google Scholar
Defant, A. and Floret, K., Tensor norms and operator ideals. North-Holland Math. Stud. 176, North-Holland Publishing Co., Amsterdam, 1993. 267, 356, 416, 646Google Scholar
Diestel, J., Geometry of Banach spaces – Selected topics, Lecture Notes in Math. 485, Springer, Berlin–Heidelberg–New York, 1975.Google Scholar
Diestel, J., Fourie, J. H., and Swart, J., The metric theory of tensor products . Grothendieck’s résumé revisited. American Mathematical Society, Providence, RI, 2008.Google Scholar
Diestel, J. and Uhl, J. J. Jr., Vector measures . Mathematical Surveys 15, American Mathematical Society, Providence, RI, 1977.Google Scholar
Dineen, S., The Schwarz lemma. Oxford Math. Monogr., Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1989. 79, 87, 88, 207, 211Google Scholar
Deville, R., Godefroy, G., and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs Surveys Pure Appl. Math. 64, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993.Google Scholar
Dixmier, J., Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann). Deuxième édition, revue et augmentée. Cahiers Scientifiques 25, Gauthier-Villars Éditeur, Paris, 1969. 492, 506Google Scholar
Dixmier, J., Les C∗-algèbres et leurs représentations. Deuxième édition. Cahiers Scientifiques 29, Gauthier-Villars Éditeur, Paris, 1969.Google Scholar
Doran, R. S. and Belfi, V. A., Characterizations of C∗-algebras: The Gelfand– Naimark theorems. Monographs Textbooks Pure Appl. Math. 101, Marcel Dekker, New York–Basel, 1986. xvii, 401Google Scholar
Dunford, N. and Schwartz, J. T., Linear operators. Part I. General theory. With the assistance of W. G. Bade and R. G. Bartle. Reprint of the 1958 original. Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1988. 12, 533, 541Google Scholar
Ebbinghaus, H.-D., Hermes, H., Hirzbruch, F., Koecher, H., Mainzer, K., Neukirch, J., Prestel, A., and Remmert, R., Numbers . Grad. Texts in Math. 123, Springer, New York, 1991. 409 Google Scholar
Elduque, A. and Myung, H. Ch., Mutations of alternative algebras . Math. Appl. 278, Kluwer Academic Publishers Group, Dordrecht, 1994.Google Scholar
Fabian, M., Habala, P., Hájek, P., Montesinos, V., and Zizler, V., Banach space theory. The basis for linear and nonlinear analysis . CMS Books Math., Springer, New York, 2011. 247, 249, 288, 338Google Scholar
Fleming, R. J. and Jamison, J. E., Isometries on Banach spaces. Vol. 1. Function spaces. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 129, Chapman & Hall/CRC, Boca Raton, FL, 2003.Google Scholar
Fleming, R. J. and Jamison, J. E., Isometries on Banach spaces. Vol. 2. Vector-valued function spaces. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 138, Chapman & Hall/CRC, Boca Raton, FL, 2008.Google Scholar
Friedmann, Y. and Scarr, T., Physical applications of homogeneous balls. Prog. Math. Phys. 40, Birhäuser, Boston, 2005. 207 Google Scholar
González, S. (ed.), Nonassociative algebra and its applications (Oviedo, 1993). Math. Appl. 303, Kluwer Academic Publishers, Dordrecht–Boston–London 1994. 679, 681, 685, 690, 702, 706Google Scholar
González, S. and Myung, H. Ch. (eds.), Nonassociative algebraic models. Proceedings of the workshop held at the Universidad de Zaragoza, Zaragoza, April 1989 . Nova Science Publishers, Inc., Commack, NY, 1992. 671, 675, 685, 701, 702, 709Google Scholar
Goodearl, K. R., Notes on real and complex C-algebras. Shiva Mathematics Series 5. Shiva Publishing Ltd., Nantwich, 1982.Google Scholar
Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. (1955), no. 16.Google Scholar
Hamilton, W. R., On quaternions, or on a new system of imaginaries in Algebra. Philosophical Magazine, (1844–1850), ed. D. R. Wilkins, 2000. http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/OnQuat/OnQuat.pdf Google Scholar
Hanche-Olsen, H. and Størmer, E., Jordan operator algebras . Monographs and Studies in Mathematics 21, Pitman, Boston, 1984. xviii, xx, xxi, 3, 8, 9, 11, 12, 13, 14, 286, 330, 332, 339, 347, 348, 362, 398, 399, 401, 416, 551Google Scholar
Harmand, P., Werner, D., and Werner, W., M-ideals in Banach spaces and Banach algebras. Lecture Notes in Math. 1547, Springer, Berlin, 1993. 19, 266, 267Google Scholar
de la Harpe, P., Classical Banach–Lie algebras and Banach–Lie groups of operators in Hilbert space. Lecture Notes in Math. 285, Springer, Berlin–New York, 1972. 554 Google Scholar
Hazewinkel, M. (ed.), Encyclopaedia of mathematics, suplement III. Kluwer Academic Publishers, 2002. 679, 685, 703Google Scholar
Helemskii, A. Ya., Banach and locally convex algebras. Translated from Russian by A. West. Oxford Sci. Publ., The Clarendon Press, Oxford University Press, New York, 1993.Google Scholar
Herstein, I. N., Topics in ring theory. The University of Chicago Press, Chicago, 1969. 367, 510Google Scholar
Herstein, I. N., Noncommutative rings. Reprint of the 1968 original. With an afterword by Lance W. Small. Carus Mathematical Monographs 15, Mathematical Association of America, Washington, DC, 1994.Google Scholar
Hille, E., Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, New York, 1948.Google Scholar
Hille, E. and Phillips, R. S., Functional analysis and semi-groups. Third printing of the revised edition of 1957. Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, Providence, RI, 1974.Google Scholar
Hoffman, K., Banach spaces of analytic functions. Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1962.Google Scholar
Iochum, B., Cônes autopolaires et algèbres de Jordan . Lecture Notes in Math. 1049, Springer, Berlin, 1984.Google Scholar
Iochum, B. and Loupias, G. (eds.), Colloque sur les algèbres de Jordan, Montpellier, Octobre 1985 . Ann. Sci. Univ. ‘Blaise Pascal’, Clermont II, Sér. Math . 27 (1991). 674, 679, 681, 685, 702Google Scholar
Iordanescu, R., Jordan structures in analysis, geometry and physics. Editura Academiei Române, Bucharest, 2009. 597 Google Scholar
Isidro, J. M. and Stachó, L. L., Holomorphic automorphism groups in Banach spaces: an elementary introduction . North-Holland Math. Stud. 105, North-Holland Publishing Co., Amsterdam, 1985. xix, 53, 87, 88, 135, 174, 207, 211Google Scholar
Jacobson, N., Lie algebras. Interscience Tracts in Pure and Applied Mathematics 10, Interscience Publishers, New York–London, 1962. 549 Google Scholar
Jacobson, N., Structure of rings. Amer. Math. Soc. Colloq. Publ. 37, Providence, RI, 1964. 500, 559, 598Google Scholar
Jacobson, N., Structure and representations of Jordan algebras . Amer. Math. Soc. Colloq. Publ. 39, Providence, RI, 1968. 472, 594, 597Google Scholar
Jacobson, N., Structure theory of Jordan algebras . University of Arkansas Lecture Notes in Mathematics 5, University of Arkansas, Fayetteville, AR, 1981. 361 Google Scholar
Jameson, G. J. O., Topology and normed spaces. Chapman and Hall, London; Halsted Press [John Wiley & Sons], New York, 1974.Google Scholar
Johnson, W. B. and Lindenstrauss, J. (eds.), Handbook of the geometry of Banach spaces. Vol. 2. North-Holland, Amsterdam, 2003. 671, 681Google Scholar
Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vol. I. Elementary theory . Grad. Stud. Math. 15, American Mathematical Society, Providence, RI, 1997. 330, 366, 459Google Scholar
Kaidi, A., Bases para una teoría de las álgebras no asociativas normadas . PhD thesis, Granada 1978. 597 Google Scholar
Kantor, I. L. and Solodovnikov, A. S., Hypercomplex numbers. An elementary introduction to algebras. Translated from Russian by A. Shenitzer. Springer, New York, 1989.Google Scholar
Kaplansky, I., Rings of operators. Math. Lecture Note Ser., W. A. Benjamin, Inc., New York–Amsterdam, 1968. xxi, 398Google Scholar
Kaplansky, I., Algebraic and analytic aspects of operator algebras. CBMS Regional Conf. Ser. in Math. 1, American Mathematical Society, Providence, RI, 1970.Google Scholar
Kargapolov, M. I. and Merzljakov, Ju. I., Fundamentals of the theory of groups. Translated from the second Russian edition by Robert G. Burns. Grad. Texts in Math. 62, Springer-Verlag, New York–Berlin, 1979. 633 Google Scholar
Kaup, W., McCrimmon, K., and Petersson, H. P. (eds.), Jordan algebras, Proceedings of the conference held in Oberwolfach, Germany, August 9–15, 1992. Walter de Gruyter, Berlin–New York, 1994. 685, 686Google Scholar
Knus, M.-A., Merkurjev, A., Rost, M., and Tignol, J.-P., The book of involutions. Amer. Math. Soc. Colloq. Publ. 44, Providence, RI, 1998.Google Scholar
Lam, T. Y., A first course in noncommutative rings. Second edition. Grad. Texts in Math. 131, Springer, New York, 2001.Google Scholar
Laursen, K. B. and Neumann, M. M., An introduction to local spectral theory. London Math. Soc. Monogr. New Series 20, Clarendon Press, Oxford, 2000. 596 Google Scholar
Li, B., Real operator algebras. World Scientific Publishing Co., Inc., River Edge, NJ, 2003. 549 Google Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. I. Sequence spaces. Ergeb. Math. Grenzgeb. 92, Springer, Berlin–New York, 1977. 261 Google Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. II. Function spaces. Ergeb. Math. Grenzgeb. 97, Springer, Berlin–New York, 1979.Google Scholar
Loos, O., Jordan pairs. Lecture Notes in Math. 460, Springer, Berlin–New York, 1975. 445 Google Scholar
Loos, O., Bounded symmetric domains and Jordan pairs. Lecture Notes, University of California, Irvine, 1977. 211, 337, 441, 444, 454, 460Google Scholar
Loy, R. J. (ed.), Conference on Automatic Continuity and Banach Algebras (Canberra, 1989). Proc. Centre Math. Anal. Austral. Nat. Univ. 21, Austral. Nat. Univ., Canberra, 1989. 672, 681Google Scholar
Martín, M., Índice numérico de un espacio de Banach . PhD thesis, Granada 2000.Google Scholar
Martínez, J., Sobre álgebras de Jordan normadas completas . PhD thesis, Granada 1977. Tesis Doctorales de la Universidad de Granada 149, Secretariado de Publicaciones de la Universidad de Granada, 1977. 597Google Scholar
Mauldin, R. D. (ed.), The Scottish book. Mathematics from the Scottish café. Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. Birkhäuser, Boston, Mass., 1981.Google Scholar
McCrimmon, K., A taste of Jordan algebras . Universitext, Springer, New York, 2004 361, 364, 401, 589, 591, 598Google Scholar
Megginson, R. E., An introduction to Banach space theory. Grad. Texts in Math. 183, Springer, New York, 1998. 7, 220, 340Google Scholar
Meyberg, A., Lectures on algebras and triple systems. Lecture notes, The University of Virginia, Charlottesville, 1972.Google Scholar
Müller, V., Spectral theory of linear operators and spectral systems in Banach algebras. Second edition. Oper. Theory Adv. Appl. 139, Birkhäuser Verlag, Basel, 2007.Google Scholar
Murphy, G. J., C-algebras and operator theory. Academic Press, Inc., Boston, MA, 1990. 330, 408Google Scholar
Myung, H. Ch., Malcev-admissible algebras . Progr. Math. 64, Birkhäuser Boston, Inc., Boston, MA, 1986.Google Scholar
Naimark, M. A., Normed algebras. Translated from the second Russian edition by Leo F. Boron. Third edition. Wolters–Noordhoff Series of Monographs and Textbooks on Pure and Applied Mathematics, Wolters–Noordhoff Publishing, Groningen, 1972. 551 Google Scholar
Ocaña, F. G., El axioma de Sakai en JV-álgebras. PhD thesis, Granada 1979. Tesis Doctorales de la Universidad de Granada 224, Secretariado de Publicaciones de la Universidad de Granada, 1979.Google Scholar
Okubo, S., Introduction to octonion and other non-associative algebras in physics. Montroll Memorial Lecture Ser. Math. Phys. 2, Cambridge University Press, Cambridge, 1995.Google Scholar
Palmer, T. W., Banach algebras and the general theory of ∗-algebras, Volume I, algebras and Banach algebras. Encyclopedia Math. Appl. 49, Cambridge University Press, Cambridge, 1994. xxvi, 650, 651, 652, 654Google Scholar
Palmer, T. W., Banach algebras and the general theory of ∗-algebras, Volume II, ∗-algebras. Encyclopedia Math. Appl. 79, Cambridge University Press, Cambridge, 2001. xvii Google Scholar
Paulsen, V., Completely bounded maps and operator algebras. Cambridge Stud. Adv. Math. 78, Cambridge University Press, Cambridge, 2002. 273 Google Scholar
Pedersen, G., Analysis now. Grad. Texts in Math. 118, Springer, New York, 1989. 330 Google Scholar
Pietsch, A., History of Banach spaces and linear operators. Birkhäuser Boston, Inc., Boston, MA, 2007. 236, 550Google Scholar
Pisier, G., Introduction to operator space theory. London Math. Soc. Lecture Note Ser. 294, Cambridge University Press, Cambridge, 2003.Google Scholar
Przeworska-Rolewicz, D., Linear spaces and linear operators. Institute of Mathematics of the Polish Academy of Sciences, Warsaw, 2007.Google Scholar
Ransford, T., Potential theory in the complex plane. London Math. Soc. Stud. Texts 28, Cambridge University Press, Cambridge, 1995.Google Scholar
Razmyslov, Yu. P., Identities of algebras and their representations. Transl. Math. Monogr. 138, American Mathematical Society, Providence, RI, 1994.Google Scholar
Rickart, C. E., General theory of Banach algebras. The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, NJ–Toronto–London–New York, 1960. 335, 481, 524, 548, 551Google Scholar
Riesz, F. and Sz-Nagy, B., Leçons d’analyse fonctionelle. Cinquième édition. Gauthier-Villars, Paris; Akadémiai Kiadó, Budapest, 1968. 330 Google Scholar
Roch, S., Santos, P. A., and Silbermann, B., Non-commutative Gelfand theories. A tool-kit for operator theorists and numerical analysts . Universitext, Springer London, Ltd., London, 2011.Google Scholar
Rodríguez, A., Contribución a la teoría de las C-álgebras con unidad . PhD thesis, Granada 1974. Tesis Doctorales de la Universidad de Granada 57, Secretariado de Publicaciones de la Universidad de Granada, 1974. 336 Google Scholar
Rodríguez, A., Números hipercomplejos en dimensión infinita . Discurso de ingreso en la Academia de Ciencias Matemáticas, Físico-Químicas y Naturales de Granada, Granada, 1993. 409 Google Scholar
Rolewicz, S., Metric linear spaces. Math. Appl. 20, D. Reidel Publishing Co., Dordrecht; PWN-Polish Scientific Publishers, Warsaw, 1985. 196 Google Scholar
Rose, H. E., Linear algebra. A pure mathematical approach. Birkhäuser Verlag, Basel, 2002.Google Scholar
Rowen, L. H., Ring theory, Volume I . Pure Appl. Math. 127. Academic Press, Inc., Boston, 1988.Google Scholar
Rudin, W., Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. 425, 433Google Scholar
Rudin, W., Functional analysis. Second edition. Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc., New York, 1991.Google Scholar
Rynne, B. P. and Youngson, M. A., Linear functional analysis . Second edition. Springer Undergrad. Math. Ser., Springer London, Ltd., London, 2008.Google Scholar
Sakai, S., C-algebras and W-algebras. Ergeb. Math. Grenzgeb. 60, Springer, New York–Heidelberg, 1971. 19, 329, 331, 339, 399, 421Google Scholar
Sakai, S., Operator algebras in dynamical systems. The theory of unbounded derivations in C-algebras. Encyclopedia Math. Appl. 41, Cambridge University Press, Cambridge, 1991.Google Scholar
Schafer, R. D., An introduction to nonassociative algebras. Corrected reprint of the 1966 original. Dover Publications, Inc., New York, 1995. 208, 360, 361, 401, 545, 652Google Scholar
Schatten, R., Norm ideals of completely continuous operators . Second printing. Ergeb. Math. Grenzgeb. 27, Springer, Berlin–New York, 1970. 409, 481, 494, 524, 531, 532, 533Google Scholar
Sinclair, A. M., Automatic continuity of linear operators. London Math. Soc. Lecture Note Ser. 21, Cambridge University Press, Cambridge–New York–Melbourne, 1976. 499 Google Scholar
Taylor, A. E. and Lay, D. C., Introduction to Functional Analysis. Second edition. John Wiley & Sons, New York–Chichester–Brisbane, 1980.Google Scholar
Tian, J. P., Evolution algebras and their applications. Lecture Notes in Math. 1921, Springer, Berlin, 2008.Google Scholar
Topping, D. M., Jordan algebras of self-adjoint operators. Mem. Amer. Math. Soc. (1965), no. 53. 400Google Scholar
Upmeier, H., Symmetric Banach Manifolds and Jordan C-algebras. North-Holland Math. Stud. 104, North-Holland, Amsterdam, 1985. xix, 52, 53, 87, 135, 174, 207, 211, 597Google Scholar
Upmeier, H. Jordan algebras in analysis, operator theory, and quantum mechanics. CBMS Regional Conf. Ser. in Math. 67, American Mathematical Society, Providence, RI, 1987. 1987. 53, 87, 135, 174, 207, 211Google Scholar
Villena, A. R., Algunas cuestiones sobre las JB∗-álgebras: centroide, centroide extendido y zócalo . PhD thesis, Granada 1990.Google Scholar
Wilansky, A., Modern methods in topological vector spaces. McGraw-Hill International Book Co., New York, 1978.Google Scholar
Wilansky, A., Topology for analysis. Reprint of the 1970 edition. Robert E. Krieger Publishing Co., Inc., Melbourne, FL, 1983.Google Scholar
Wisbauer, R., Modules and algebras: bimodule structure and group actions on algebras. Pitman Monographs Surveys Pure Appl. Math. 81, Longman, Harlow, 1996.Google Scholar
Zelazko, W., Banach algebras. Translated from Polish by Marcin E. Kuczma. Elsevier Publishing Co., Amsterdam–London–New York; PWN-Polish Scientific Publishers, Warsaw, 1973.Google Scholar
Zemánek, J., Properties of the spectral radius in Banach algebras. PhD thesis, Warszawa 1977.Google Scholar
Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P., and Shirshov, A. I., Rings that are nearly associative. Translated from Russian by Harry F. Smith. Pure Appl. Math. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York–London, 1982. 360, 361, 401, 413, 414, 415, 570, 571, 597, 631, 636, 647Google Scholar
Aarnes, J. F., On the Mackey-topology for a von Neumann algebra. Math. Scand . 22 (1968), 87107. 332Google Scholar
Acosta, M. D., An inequality for norm of operators. Extracta Math . 10 (1995), 115–8. 469Google Scholar
Acosta, M. D., Denseness of norm attaining mappings. RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat . 100 (2006), 930. 338Google Scholar
Akemann, C. A., The dual space of an operator algebra. Trans. Amer. Math. Soc . 126 (1967), 286302. xx, 268, 274, 332, 334, 335Google Scholar
Albert, A. A., A theory of trace-admissible algebras. Proc. Nat. Acad. Sci. USA 35 (1949), 317–22. Reprinted in [692], pp. 491–6. 545Google Scholar
Albert, A. A. and Jacobson, N., On reduced exceptional simple Jordan algebras. Ann. of Math . 66 (1957), 400–17. Reprinted in [692], pp. 677–94. 361Google Scholar
Albrecht, E. and Dales, H. G., Continuity of homomorphisms from C∗-algebras and other Banach algebras. In Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981), pp. 375–96, Lecture Notes in Math. 975, Springer, Berlin-New York, 1983. 549Google Scholar
Alfsen, E. M. and Effros, E. G., Structure in real Banach spaces. I, II. Ann. of Math . 96 (1972), 98128; ibid. 96 (1972), 129–73. 19, 398Google Scholar
Allison, B. N., A class of nonassociative algebras with involution containing the class of Jordan algebras. Math. Ann . 237 (1978), 133–56. 555Google Scholar
Allison, B. N., Models of isotropic simple Lie algebras. Comm. Algebra 7 (1979), 1835–75. 555Google Scholar
Allison, B. N. and Faulkner, J. R., The algebra of symmetric octonion tensors. Nova J. Algebra Geom . 2 (1993), 4757. 555Google Scholar
Anquela, J. A., Cabrera, M., and Moreno, A., Eater ideals in Jordan algebras. J. Pure Appl. Algebra 125 (1998), 117. 464Google Scholar
Ara, P., The extended centroid of C -algebras. Archiv. Math . 54 (1990), 358–64. 408Google Scholar
Ara, P., On the symmetric algebra of quotients of a C -algebra. Glasgow Math. J. 32 (1990), 377–9. 408Google Scholar
Arazy, J., An application of infinite-dimensional holomorphy to the geometry of Banach spaces. In Geometrical aspects of functional analysis (1985/86), pp. 122–50, Lecture Notes in Math. 1267, Springer, Berlin, 1987. xix, 87, 135, 174, 207Google Scholar
Arens, R. and Goldberg, G., Quadrative seminorms and Jordan structures on algebras. Linear Algebra Appl . 181 (1993), 269–78. 470Google Scholar
Aupetit, B., Analytic multivalued functions in Banach algebras and uniform algebras. Adv. Math . 44 (1982), 1860. 603Google Scholar
Aupetit, B., Some uses of subharmonicity in functional analysis. In Spectral theory (Warsaw, 1977), pp. 31–7, Banach Center Publ. 8, Polish Acad. Sci. Inst. Math., Warsaw, 1982. 603Google Scholar
Aupetit, B., Inessential elements in Banach algebras. Bull. London Math. Soc . 18 (1986), 493–7. 599Google Scholar
Aupetit, B., Spectral characterization of the radical in Banach and Jordan-Banach algebras. Math. Proc. Cambridge Philos. Soc . 114 (1993), 31–5. 603Google Scholar
Aupetit, B., Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras. J. London Math. Soc . 62 (2000), 917–24. 603Google Scholar
Aupetit, B. and Mouton, H. du T., Trace and determinant in Banach algebras. Studia Math . 121 (1996), 115–36. 601Google Scholar
Aupetit, B. and Zraïbi, A., Propriétés analytiques du spectre dans les algèbres de Jordan-Banach. Manuscripta Math . 38 (1982), 381–6. 596, 597Google Scholar
Bachelis, G. F., Homomorphisms of annihilator Banach algebras. Pacific J. Math . 25 (1968), 229–47. xxv, 584Google Scholar
Bade, W. G., Curtis, P. C. JR., and Sinclair, A. M., Raising bounded groups and splitting of radical extensions of conmmutative Banach algebras. Studia Math . 141 (1) (2000), 8598. 651Google Scholar
Baker, J. W. and Pym, J. S., A remark on continuous bilinear mappings. Proc. Edinburgh Math. Soc . 17 (1970/71), 245–8. 436Google Scholar
Bakić, D. and Guljaš, B., Operators on Hilbert H -modules. J. Operator Theory 46 (2001), 123–37. 557Google Scholar
Balachandran, V. K., Automorphisms of L -algebras. Tôhoku Math. J . 22 (1970), 163–73. 549Google Scholar
Balachandran, V. K., Real L -algebras. Indian J. Pure Appl. Math . 3 (1972), 1224–46. 554Google Scholar
Barton, T. J., Dang, T., and Horn, G., Normal representations of Banach Jordan triple systems. Proc. Amer. Math. Soc . 102 (1988), 551–5. 211, 241Google Scholar
Barton, T. J. and Friedman, Y., Grothendieck’s inequality for JB -triples and applications. J. London Math. Soc . 36 (1987), 513–23. xx, 268, 274, 275, 337, 338, 345, 346Google Scholar
Barton, T. J. and Timoney, R. M., Weak∗-continuity of Jordan triple products and its applications. Math. Scand . 59 (1986), 177–91. xix, 2, 211, 236, 237Google Scholar
Beidar, K. I., Mikhalev, A. V., and Slinko, A. M., A criterion for primeness of nondegenerate alternative and Jordan algebras. Trudy Moskov. Mat. Obshch . 50 (1987), 130–7; translation in Trans. Moscow Math. Soc. 50 (1988), 129–37. xxii, 408, 468Google Scholar
Benkart, G., On inner ideals and ad-nilpotent elements of Lie algebras. Trans. Amer. Math. Soc . 232 (1977), 6181. 600Google Scholar
Benslimane, M. and Boudi, N., Isomorphisms of Jordan-Banach algebras. Extracta Math . 11 (1996), 414–6. 603Google Scholar
Benslimane, M. and Boudi, N., Ring isomorphisms of Jordan-Banach algebras. In Commutative ring theory (Fès, 1995), pp. 105–11, Lect. Notes Pure Appl. Math. 185, Dekker, New York, 1997. 603Google Scholar
Benslimane, M. and Mesmoudi, L., Characterization of commutative normed algebras. In [705], pp. 53–7. 436Google Scholar
Benslimane, M., Mesmoudi, L., and Rodríguez, A., A characterization of commutativity for non-associative normed algebras. Extracta Math . 15 (2000), 121–43. xxii, 436Google Scholar
Berger, M. A. and Wang, Y., Bounded semigroups of matrices. Linear Algebra Appl . 166 (1992), 21–7. 651Google Scholar
Blecher, D. P. and Paulsen, V. I., Multipliers of operator spaces, and the injective envelope. Pacific J. Math . 200 (2001), 117. 273Google Scholar
Bombal, F., On (V) sets and Pełczyński’s property (V). Glasgow Math. J. 32 (1990), 109–20. 266Google Scholar
Bonsall, F. F. and Goldie, A. W., Annihilator algebras. Proc. London Math. Soc . 4 (1954), 154–67. 584Google Scholar
Boudi, N., Marhnine, H., and Zarhouti, C., Additive derivations on Jordan Banach pairs. Comm. Algebra 32 (2004), 3609–25. 466, 603Google Scholar
Boyadjiev, H. N. and Youngson, M. A., Alternators on Banach Jordan algebras. C. R. Acad. Bulgare Sci . 33 (1980), 1589–90. 400Google Scholar
Braun, R., Kaup, W., and Upmeier, H., On the automorphisms of circular and Reinhardt domains in complex Banach spaces. Manuscripta Math . 25 (1978), 97133. 207Google Scholar
Brešar, M., Functional identities: A survey. Contemp. Math . 259 (2000), 93109. 602Google Scholar
Brešar, M. and Villena, A. R., The range of a derivation on a Jordan-Banach algebra. Studia Math . 146 (2001), 177200. 466, 707Google Scholar
Bunce, L. J., The theory and structure of dual JB-algebras. Math. Z. 180 (1982), 525–34. 584, 598Google Scholar
Bunce, L. J., On compact action in JB-algebras. Proc. Edinburgh Math. Soc . 26 (1983), 353–60. 400Google Scholar
Bunce, L. J., Norm preserving extensions in JBW -triple preduals. Quart. J. Math. Oxford 52 (2001), 133–6. 338, 339, 346Google Scholar
Bunce, L. J. and Chu, C.-H., Compact operations, multipliers and Radon-Nikodym property in JB -triples. Pacific J. Math . 153 (1992), 249–65. xx, 275, 346, 450, 459, 461Google Scholar
Bunce, L. J. and Chu, C.-H., Real contractive projections on commutative C -algebras. Math. Z . 226 (1997), 85101. 210Google Scholar
Bunce, L. J., Chu, C.-H., Stachó, L. L., and Zalar, B., On prime JB -triples. Quart. J. Math. Oxford 49 (1998), 279–90. 409Google Scholar
Cabello, J. C. and Cabrera, M., Structure theory for multiplicatively semiprime algebras. J. Algebra 282 (2004), 386421. xxv, 546, 584Google Scholar
Cabello, J. C., Cabrera, M., and Fernández, A., π-complemented algebras through pseudocomplemented lattices. Order 29 (2012), 463–79. 585Google Scholar
Cabello, J. C., Cabrera, M., López, G., and Martindale, W. S. III, Multiplicative semiprimeness of skew Lie algebras. Comm. Algebra 32 (2004), 3487–501. 546Google Scholar
Cabello, J. C., Cabrera, M., and Nieto, E., ε-complemented algebras. J. Algebra 349 (2012), 234–67. 546, 585Google Scholar
Cabello, J. C., Cabrera, M., Rodríguez, A., and Roura, R., A characterization of π-complemented algebras. Comm. Algebra 41 (2013), 3067–79. 585Google Scholar
Cabello, J. C., Cabrera, M., and Roura, R., A note on the multiplicative primeness of degenerate Jordan algebras. Sib. Math. J . 51 (2010), 818–23. 546Google Scholar
Cabello, J. C., Cabrera, M., and Roura, R., π-complementation in the unitisation and multiplication algebras of a semiprime algebra. Comm. Algebra 40 (2012), 3507–31. 546Google Scholar
Cabrera, M., El Marrakchi, A., Martínez, J., and Rodríguez, A.. Bounded differential operators on Hilbert modules and derivations of structurable H -algebras. Comm. Algebra 21 (1993), 2905–45. 559Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Hilbert modules over H -algebras in relation with Hilbert ternary rings. In [734], pp. 33–44. 558Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Hilbert modules revisited: orthonormal bases and Hilbert–Schmidt operators. Glasgow Math. J . 37 (1995), 4554. 557Google Scholar
Cabrera, M. and Mohammed, A. A., Extended centroid and central closure of the multiplication algebra. Comm. Algebra 27 (1999), 5723–36. 546, 576Google Scholar
Cabrera, M. and Mohammed, A. A., A representation theorem for algebras with commuting involutions. Linear Algebra Appl . 306 (2000), 2531. 476Google Scholar
Cabrera, M. and Mohammed, A. A., Extended centroid and central closure of multiplicatively semiprime algebras. Comm. Algebra 29 (2001), 1215–33. 546Google Scholar
Cabrera, M. and Mohammed, A. A., Totally multiplicatively prime algebras. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 1145–62. xxiii, 408, 546, 547, 549Google Scholar
Cabrera, M. and Mohammed, A. A., Algebra of quotients with bounded evaluation of a normed prime algebra. In: Operator theory and Banach algebras. Proceedings of the International Conference in Analysis, Rabat (Moroco), April 12–14, 1999 (eds. Chidami, M., Curto, R., Mbekhta, M., Vasilescu, F.-H. and Zemánek, J.). Theta Found., Bucharest, 2003, pp. 3950. 547Google Scholar
Cabrera, M. and Mohammed, A. A., Algebras of quotients with bounded evaluation of a normed semiprime algebra. Studia Math . 154 (2003), 113–35. 547Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., On primitive Jordan-Banach algebras. In [733], pp. 54–9. 463Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., On the behaviour of Jordan-algebra norms on associative algebras. Studia Math . 113 (1995), 81100. xxii, 469, 470, 471, 474Google Scholar
Cabrera, M. and Rodríguez, A., A characterization of the centre of a nondegenerate Jordan algebra. Comm. Algebra 21 (1993), 359–69. 469Google Scholar
Cabrera, M. and Rodríguez, A., Zel’manov’s theorem for nondegenerately ultraprime Jordan-Banach algebras. In [733], pp. 60–5. 462Google Scholar
Cabrera, M. and Villena, A. R., Multiplicative-semiprimeness of nondegenerate Jordan algebras. Comm. Algebra 32 (2004), 39954003. 546Google Scholar
Cao, P. and Turovskii, Yu. V., Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras. Studia Math . 235 (2016), 171208. 603, 652Google Scholar
Cartan, É., Sur les domaines bornes homogenes de l’espace de n variables complexes. Abh. Math. Sem. Univ. Hamburg 11 (1935), 116–62. 210Google Scholar
Cartan, H., Les fonctions de deux variables complexes et le problème de la représentation analytique. J. Math. Pures Appl ., 9 e série, 10 (1931), 1114. 87Google Scholar
Castellón, A. and Cuenca, J. A., Compatibility in Jordan H -triple systems. Boll. Un. Mat. Ital. B 4 (1990), 433–47. 560Google Scholar
Castellón, A. and Cuenca, J. A., Alternative H -triple systems. Comm. Algebra 20 (1992), 3191–206. 561Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Ternary H -algebras. Boll. Un. Mat. Ital. B 6 (1992), 217–28. 559Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Jordan H -triples. In [733], pp. 66–72. 549, 560Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Special Jordan H -triple system. Comm. Algebra 28 (2000), 4699–706. 560Google Scholar
Chaperon, M., On the Cauchy–Kowalevski theorem. Enseign. Math . 55 (2009), 359–71. 137Google Scholar
Chu, C.-H. and Iochum, B., Weakly compact operators on Jordan triples. Math. Ann . 281 (1988), 451–8. 335, 340, 341Google Scholar
Chu, C.-H. and Iochum, B., Complementation of Jordan triples in von Neumann algebras. Proc. Amer. Math. Soc . 108 (1990), 1924. 336Google Scholar
Chu, C.-H., Moreno, A., and Rodríguez, A., On prime real JB -triples. In Function spaces (Edwardsville, IL, 1998), pp. 105–9, Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999. 346Google Scholar
Cohen, P. J., Factorization in group algebras. Duke Math. J . 26 (1959), 199205. 659Google Scholar
Crabb, M. J., A new prime C -algebra that is not primitive. J. Funct. Anal . 236 (2006), 630–3. 467Google Scholar
Cuenca, J. A., Sur la théorie de structure des H -algèbres de Jordan non commutatives. In [749], pp. 143–52. 553Google Scholar
Cuenca, J. A., Moufang H -algebras. Extracta Math . 17 (2002), 239–46. 552Google Scholar
Cuenca, J. A., García, A., and Martín, C., Jacobson density for associative pairs and its applications. Comm. Algebra 17 (1989), 2595–610. 560Google Scholar
Cuenca, J. A., García, A., and Martín, C., Prime associative superalgebras with nonzero socle. Algebras Groups Geom . 11 (1994), 359–69. 560Google Scholar
Cuenca, J. A. and Martín, C., Jordan two-graded H -algebras. In [734], pp. 91–100. 559, 560Google Scholar
Cuenca, J. A. and Miguel, F., On a Hopf’s theorem. Preprint 2016. 409Google Scholar
Cuenca, J. A. and Sánchez, A., Structure theory for real noncommutative Jordan H -algebras. J. Algebra 164 (1994), 481–99. 553Google Scholar
Cuntz, J., On the continuity of semi-norms on operator algebras. Math. Ann . 220 (1976), 171–83. 399Google Scholar
Curto, R. E., Spectral theory of elementary operators. In Elementary operators and applications (Blaubeuren, 1991) (Ed. by Mathieu, M.), pp. 352, World Sci. Publ., River Edge, NJ, 1992. 635Google Scholar
D’Amour, A., Quadratic Jordan systems of Hermitian type. J. Algebra 149 (1992), 197233. xxii, 438, 448, 459, 461Google Scholar
D’Amour, A. and McCrimmon, K., The structure of quadratic Jordan systems of Clifford type. J. Algebra 234 (2000), 3189. xxii, 438, 452, 453, 454, 459Google Scholar
Dieudonné, J., Sur le socle d’un anneau et les anneaux simples infinis. Bull. Soc. Math. France 70 (1942), 4675. 598Google Scholar
Dineen, S., Complete holomorphic vector fields on the second dual of a Banach space. Math. Scand . 59 (1986), 131–42. 236Google Scholar
Dineen, S. and Timoney, R. M., The centroid of a JB -triple system. Math. Scand . 62 (1988), 327–42. 346Google Scholar
Dineen, S. and Timoney, R. M., The algebraic metric of Harris on JB -triple systems. Proc. Roy. Irish Acad. Sect. A 90 (1990), 8397. 558Google Scholar
Dixmier, J., Sur les C -algèbres. Bull. Soc. Math. France 88 (1960), 95112. 467Google Scholar
Dixon, P. G., Topologically nilpotent Banach algebras and factorization. Proc. Roy. Soc. Edinburgh Sect A 119 (1991), 329–41. xxvi, 650, 651, 654, 655, 657Google Scholar
Dixon, P. G. and Müller, V., A note on topologically nilpotent Banach algebras. Studia Math . 102 (1992), 269–75. xxvi, 623, 650, 651, 653Google Scholar
Dixon, P. G. and Willis, G. A., Approximate identities in extensions of topologically nilpotent Banach algebras. Proc. Roy. Soc. Edinburgh 122A (1992), 4552. xxvi, 650, 651Google Scholar
Doran, R. S. and Wichmann, J., The Gelfand–Naimark theorems for C -algebras. Enseignement Math . 23 (1977), 153–80. xviiGoogle Scholar
Draper, C., Fernández, A., García, E., and Gómez, M., The socle of a nondegenerate Lie algebra. J. Algebra 319 (2008), 2372–94. 600Google Scholar
Edgar, G. A., An ordering for the Banach spaces. Pacific J. Math . 108 (1983), 8398. 266Google Scholar
Edwards, C. M. and Rüttimann, G. T., A characterization of inner ideals in JB -triples. Proc. Amer. Math. Soc . 116 (1992), 1049–57. 339Google Scholar
El Kinani, A. and Oudadess, M., Un critère généralisé de Le Page et commutativité. C. R. Math. Rep. Acad. Sci. Canada 18 (1996), 71–4. 436Google Scholar
El Marrakchi, A., Sur l’unité approchée des H∗-algèbres structurables avec annulateur zéro. Int. J. Math. Game Theory Algebra 13 (2003), 267–79. 556Google Scholar
Elsner, L., The generalized spectral-radius theorem: an analytic-geometric proof. Linear Algebra Appl . 220 (1995), 151–9. 651Google Scholar
Emmanuele, G., On the Banach spaces with the property (V ) of Pełczyński. Ann. Mat. Pura Appl . 152 (1988), 171–81. 266Google Scholar
Essaleh, A. B. A., Peralta, A. M., and Ramírez, M. I., Pointwise-generalized-inverses of linear maps between C -algebras and JB -triples. Operators and Matrices (to appear). 273, 274Google Scholar
Fernández, A., Banach-Jordan pair. In [741], pp. 57–8. 462, 600Google Scholar
Fernández, A., A Jordan approach to finitary Lie algebras. Quart. J. Math . 67 (2016), 565–71. 600Google Scholar
Fernández, A. and García, E., Algebraic lattices and nonassociative structure. Proc. Amer. Math. Soc . 126 (1998), 3211–21. 584Google Scholar
Fernández, A., García, E., and Gómez, M., The Jordan algebras of a Lie algebra. J. Algebra 308 (2007), 164–77. 600Google Scholar
Fernández, A., García, E., Sánchez, E., and Siles, M., Strong regularity and Hermitian Hilbert triples. Quart. J. Math. Oxford 45 (1994), 4355. 558Google Scholar
Fernández, A. and Golubkov, A. Yu., Lie algebras with an algebraic adjoint representation revisited. Manuscripta Math . 140 (2013), 363–76. 600Google Scholar
Fernández, A., Marhnine, H., and Zarhouti, C., Derivations on Banach-Jordan pairs. Quart. J. Math. Oxford 52 (2001), 269–83. 466, 603Google Scholar
Fernández, A. and Tocón, M. I., Pseudocomplemented semilatices, boolean algebras, and compatible products. J. Algebra 242 (2001), 6091. 584Google Scholar
Fernández, A. and Tocón, M. I., Strongly prime Jordan pairs with nonzero socle. Manuscripta Math . 111 (2003), 321–40. 600Google Scholar
Fernández-Polo, F. J., Garcés, J. J., Peralta, A. M., and Villanueva, I., Tingley’s problem for spaces of trace class operators. Linear Algebra Appl . 529 (2017), 294323. 550Google Scholar
Filippov, V. T., On the theory of Mal’cev algebras. Algebra i Logika 16 (1977), 101–8. 555Google Scholar
Finston, D., On multiplication algebras. Trans. Amer. Math. Soc . 293 (1986), 807–18. 546Google Scholar
Friedman, Y. and Russo, B., Contractive projections on operator triple systems. Math. Scand . 52 (1983), 279311. 210, 331Google Scholar
Garimella, R. V., On continuity of derivations and epimorphisms on some vector-valued group algebras. Bull. Austral. Math. Soc . 56 (1997), 209–15. 596Google Scholar
Giellis, G. R., A characterization of Hilbert modules. Proc. Amer. Math. Soc . 36 (1972), 440–2. 556Google Scholar
Godefroy, G., Épluchabilité et unicité du prédual. Séminaire Choquet, 17e année (1977/78), Initiation á l’analyse, Fasc. 2, Comm. No. 11, 3 pp., Secrétariat Math., Paris, 1978. 8 Google Scholar
Godefroy, G., Parties admissibles d’un espace de Banach. Applications. Ann. Sci. École Norm. Sup. (4) 16 (1983), 109–22. 237, 267Google Scholar
Godefroy, G., Existence and uniqueness of isometric preduals: a survey. In Banach space theory (Iowa City, IA, 1987) (Ed. by Lin, B.-L.), pp. 131–93, Contemp. Math., 85, Amer. Math. Soc., Providence, 1989. 238, 241Google Scholar
Godefroy, G. and Iochum, B., Arens-regularity of Banach algebras and the geometry of Banach spaces. J. Funct. Anal . 80 (1988), 4759. xix, 245, 267, 421Google Scholar
Godefroy, G. and Saab, P., Quelques espaces de Banach ayant les propriétés (V) ou (V ) de A. Pełczyński. C. R. Acad. Sci. Paris Sér. I Math . 303 (1986), 503–6. 245, 266Google Scholar
Godefroy, G. and Saab, P., Weakly unconditionally convergent series in M-ideals. Math. Scand . 64 (1989), 307–18. 266Google Scholar
Godefroy, G. and Talagrand, M., Classes d’espaces de Banach à prédual unique. C. R. Acad. Sci. Paris Sér. I Math . 292 (1981), 323–5. 238Google Scholar
Godefroy, G. and Talagrand, M., Nouvelles classes d’espaces de Banach à prédual unique. Séminaire d’Analyse Fonctionnelle de l’École Polytechnique, 1980/81. 238, 239, 240, 241Google Scholar
Gorin, E. A. and Lin, V. Ja., A condition on the radical of a Banach algebra guaranteeing strong decomposability. (Russian) Mat. Zametki 2 (1967), 589–592; translation in Mathematical Notes 2 (1967), 851–2. 651Google Scholar
Grabiner, S., Finitely generated, Noetherian, and Artinian Banach modules. Indiana Univ. Math. J . 26 (1977), 413–25. 601Google Scholar
Grothendieck, A., Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8 (1953), 179. Reprinted in Resenhas 2 (1996), 401–80. xx, 275, 342, 343Google Scholar
Grothendieck, A., Sur les applications linéaires faiblement compactes d’espaces du type C(K). Canadian J. Math . 5 (1953), 129–73. 334Google Scholar
Gulick, S. L., Commutativity and ideals in the biduals of topological algebras. Pacific J. Math . 18 (1966), 121–37. 268Google Scholar
Haagerup, U., Solution of the similarity problem for cyclic representations of C∗-algebras. Ann. Math . 118 (1983), 215–40. 342Google Scholar
Haagerup, U., The Grothendieck inequality for bilinear forms on C -algebras. Adv. in Math . 56 (1985), 93116. 343, 344Google Scholar
Haagerup, U. and Hanche-Olsen, H., Tomita–Takesaki theory for Jordan algebras. J. Operator Theory 11 (1984), 343–64. 339Google Scholar
Haagerup, U. and Itoh, T., Grothendieck type norms for bilinear forms on C -algebras. J. Operator Theory 34 (1995), 263–83. 342Google Scholar
de la Harpe, P., Classification des L -algèbres semi-simples réelles séparables. C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A1559–61. 554Google Scholar
Harris, L. A., Schwarz’s lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A . 62 (1969), 1014–7. 207Google Scholar
Harris, L. A., A continuous form of Schwarz’s lemma in normed linear spaces. Pacific J. Math . 38 (1971), 635–9. 207Google Scholar
Harris, L. A., Analytic invariants and the Schwarz–Pick inequality. Israel J. Math . 34 (1979), 177–97. 558Google Scholar
Harris, L. A., A generalization of C -algebras. Proc. London Math. Soc . 42 (1981), 331–61. 459Google Scholar
Henriksen, M., A simple characterization of commutative rings without maximal ideals. Amer. Math. Monthly 82 (1975), 502–5. 659Google Scholar
Henson, C. W. and Moore, L. C., Jr., Subspaces of the nonstandard hull of a normed space. Trans. Amer. Math. Soc . 197 (1974), 131–43. 236Google Scholar
Hessenberger, G., Analytic properties of the spectrum in Banach Jordan systems. Collect. Math . 47 (1996), 277–84. 603Google Scholar
Horn, G., Characterization of the predual and ideal structure of a JBW -triple. Math. Scand . 61 (1987), 117–33. xix, 2, 211, 237, 238, 239, 241Google Scholar
Horn, G. and Neher, E., Classification of continuous JBW -triples. Trans. Amer. Math. Soc . 306 (1988), 553–78. 340, 344, 459Google Scholar
Jacobson, N., A note on non-associative algebras. Duke Math. J . 3 (1937), 544–8. 545Google Scholar
James, R. C., Uniformly non-square Banach spaces. Ann. of Math . 80 (1964), 542–50. 261Google Scholar
Jamjoom, F. B., Peralta, A. M., and Siddiqui, A. A., Jordan weak amenability and orthogonal forms on JB -algebras. Banach J. Math. Anal . 9 (2015), 126–45. 346Google Scholar
Jamjoom, F. B., Peralta, A. M., Siddiqui, A. A., and Tahlawi, H. M., Approximation and convex decomposition by extremals and the λ-function in JBW -triples. Quart. J. Math. Oxford 66 (2015), 583603. 346Google Scholar
Jarchow, H., Weakly compact operators on C(K) and C -algebras. In Functional analysis and its applications (Nice, 1986) (Ed. by Hogbe-Nlend, H.), pp. 263–99, ICPAM Lecture Notes, World Sci. Publishing, Singapore, 1988. 274, 335Google Scholar
Jeang, J.-S. and Ko, C.-C., On the commutativity of C -algebras. Manuscripta Math . 115 (2004), 195–8. 401Google Scholar
Ji, G. and Tomiyama, J., On characterizations of commutativity of C -algebras. Proc. Amer. Math. Soc . 131 (2003), 3845–9. 401Google Scholar
Johnson, W. B., Rosenthal, H. P., and Zippin, M., On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math . 9 (1971), 488506. 236Google Scholar
Kadison, R. V., Operator algebras with a faithful weakly-closed representation. Ann. of Math . 64 (1956), 175–81. 19Google Scholar
Kalton, N. J., Rademacher series and decoupling. New York J. Math . 11 (2005), 563–95. 343Google Scholar
Kantrowitz, R. and Neumann, M. M., Automatic continuity of homomorphisms and derivations on algebras of continuous vector-valued functions. Czechoslovak Math. J . 45 ( 120 ) (1995), 747–56. 596Google Scholar
Kaplansky, I., Regular Banach algebras. J. Indian Math. Soc . 12, (1948), 5762. 597Google Scholar
Kaup, W., Jordan algebras and holomorphy. In Functional analysis, holomorphy, and approximation theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978) (Ed. by Machado, S.), pp. 341–65, Lecture Notes in Math., 843, Springer, Berlin, 1981. 211Google Scholar
Kaup, W., Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension. I. Math. Ann . 257 (1981), 463–86. II Math. Ann. 262 (1983), 57–75. 211, 557Google Scholar
Kaup, W., Hermitian Jordan triple systems and the automorphisms of bounded symmetric domains. In [733], pp. 204–14. 210Google Scholar
Kaup, W., On spectral and singular values in JB -triples. Proc. Roy. Irish Acad. Sect. A 96 (1996), 95103. 210Google Scholar
Kaup, W. and Upmeier, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc. Amer. Math. Soc . 58 (1976), 129–33. 207Google Scholar
Kissin, E., Shulman, V. S., and Turovskii, Yu. V., Topological radicals and Frattini theory of Banach Lie algebras. Integral Equations Operator Theory 74 (2012), 51121. 652Google Scholar
Le Page, C., Sur quelques conditions entraînant la commutativité dans les algèbres de Banach. C. R. Acad. Sci. Paris Sér. A–B 265 (1967), A235A237. xxii, 347, 423, 436Google Scholar
Lin, C. S., On commutativity of C -algebras. Glasgow Math. J . 29 (1987), 93–7. 400Google Scholar
Lindenstrauss, J., On operators which attain their norm. Israel J. Math . 1 (1963), 139148. xx, 274, 337, 338Google Scholar
Lindenstrauss, J. and Rosenthal, H. P., The L p -spaces. Israel J. Math . 7 (1969), 325–49. 236Google Scholar
Loos, O., On the socle of a Jordan pair. Collect. Math . 40 (1989), 109–25. 599, 601Google Scholar
Loos, O., Finiteness conditions in Jordan pairs. Math. Z . 206 (1991), 577–87. 558Google Scholar
Loos, O. and Neher, E., Complementation of inner ideals in Jordan pairs. J. Algebra 166 (1994), 255–95. 601Google Scholar
Mackey, M. and Mellon, P., A Schwarz lemma and composition operators. Integral Equations Operator Theory 48 (2004), 511–24. 210Google Scholar
Maouche, A., Extension d’un théorème de Harte et applications aux algèbres de Jordan-Banach. Monatsh. Math . 122 (1996), 205–13. 603Google Scholar
Maouche, A., Diagonalization in Banach algebras and Jordan-Banach algebras. Extracta Math . 19 (2004), 257–60. 603Google Scholar
Martín, M., Norm-attaining compact operators. J. Funct. Anal . 267 (2014), 1585–92. 338Google Scholar
Martínez, J., Derivations of structurable H -algebras. In: Nonassociative algebra and its applications (São Paulo, 1998), pp. 219–27, Lecture Notes in Pure and Appl. Math. 211, Dekker, New York, 2000. 559Google Scholar
Mathieu, M., Weakly compact homomorphisms from C -algebras are of finite rank. Proc. Amer. Math. Soc . 107 (1989), 761–2. 336Google Scholar
Mathieu, M., Elementary operators on prime C -algebras, I. Math. Ann . 284 (1989), 223–44. xxi, 408Google Scholar
Mathieu, M., The symmetric algebra of quotients of an ultraprime Banach algebra. J. Austral. Math. Soc. Ser. A 50 (1991), 7587. 468, 469, 547Google Scholar
Mathieu, M., Review of [869]. MR1853520 (2002k:46123). 466Google Scholar
Mathieu, M. and Runde, V., Derivations mapping into the radical. II. Bull. London Math. Soc . 24 (1992), 485–7. 466Google Scholar
McCrimmon, K., On Herstein’s theorems relating Jordan and associative algebras. J. Algebra 13 (1969), 382–92. 367Google Scholar
McCrimmon, K., A characterization of the radical of a Jordan algebra. J. Algebra 18 (1971), 103–11. 597Google Scholar
McCrimmon, K., The Zel’manov approach to Jordan homomorphisms of associative algebras. J. Algebra 123 (1989), 457–77. 465Google Scholar
Neumann, M. M. and Velasco, M. V., Continuity of epimorphisms and derivations on vector-valued group algebras. Arch. Math. (Basel) 68 (1997), 151–8. 596Google Scholar
Miziolek, J. K., Müldner, T., and Rek, A., On topologically nilpotent algebras. Studia Math . 43 (1972), 4150. xxvi, 650, 651Google Scholar
Mocanu, Gh., Sur certains types de commutativité dans les algèbres de Banach. An. Univ. Bucuresti Mat. 37 (1988), 3641. 436Google Scholar
Mohammadzadeh, S. and Vishki, H. R. E., Arens regularity of module actions and the second adjoint of a derivation. Bull. Aust. Math. Soc . 77 (2008), 465–76. 268Google Scholar
Molnár, L., Modular bases in a Hilbert A-module. Czechoslovak Math. J . 42 (117) (1992), 649–56. 557Google Scholar
Molnár, L., A few conditions for a C -algebra to be commutative. Abstr. Appl. Anal. 2014, Art. ID 705836, 4 pp. 401Google Scholar
Moreno, A., Extending the norm from special Jordan triple systems to their associative envelopes. In Banach algebras’97 (Blaubeuren), pp. 363–75, de Gruyter, Berlin, 1998. xxiii, 475, 476Google Scholar
Moreno, A., The triple-norm extension problem: the nondegenerate complete case. Studia Math . 136 (1999), 91–7. xxiii, 475, 476Google Scholar
Moreno, A., Some recent results about the norm extension problem. In [705], pp. 125–31. xxiii, 462, 474, 475Google Scholar
Moreno, A. and Rodríguez, A., The norm extension problem: positive results and limits. II Congress on Examples and Counterexamples in Banach Spaces (Badajoz, 1996). Extracta Math . 12 (1997), 165–71. 462, 473, 474Google Scholar
Moreno, A. and Rodríguez, A., Algebra norms on tensor products of algebras, and the norm extension problem. Linear Algebra Appl . 269 (1998), 257305. xxiii, 472, 473, 474, 475Google Scholar
Müller, V., Nil, nilpotent and PI-algebras. In [1189], pp. 259–65. xxvi, 651Google Scholar
Neufang, M., On Mazur’s property and property (X). J. Operator Theory 60 (2008), 301–16. 238, 239Google Scholar
Ogasawara, T., A theorem on operator algebras. J. Sci. Hiroshima Univ. Ser. A . 18 (1955), 307–9. 400Google Scholar
Osborn, J. M. and Racine, M. L., Jordan rings with nonzero socle. Trans. Amer. Math. Soc . 251 (1979), 375–87. 598Google Scholar
Oudadess, M., Commutativité de certaines algèbres de Banach. Bol. Soc. Mat. Mexicana 28 (1983), 914. 436Google Scholar
Pedersen, G. K. and Størmer, E., Traces on Jordan algebras. Canad. J. Math . 34 (1982), 370–3. 339Google Scholar
Pełczyński, A., Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Acad. Polon. Sci . 10 (1962), 641–8. 266Google Scholar
Peralta, A. M., Little Grothendieck’s theorem for real JB -triples. Math. Z . 237 (2001), 531–45. 337, 346Google Scholar
Peralta, A. M., New advances on the Grothendieck’s inequality problem for bilinear forms on JB -triples. Math. Inequal. Appl . 8 (2005), 721. 346Google Scholar
Peralta, A. M., Some remarks on weak compactness in the dual space of a JB -triple. Tôhoku Math. J . 58 (2006), 149–59. 335, 340Google Scholar
Peralta, A. M. and Rodríguez, A., Grothendieck’s inequalities for real and complex JBW -triples. Proc. London Math. Soc . 83 (2001), 605–25. xx, 268, 274, 338, 340, 341, 342, 344, 345, 346Google Scholar
Peralta, A. M. and Rodríguez, A., Grothendieck’s inequalities revisited. In [1141], pp. 409–23. 346Google Scholar
Pérez de Guzmán, I., Structure theorems for alternative H -algebras. Math. Proc. Cambridge Philos. Soc. 94 (1983), 437–46. xxv, 549Google Scholar
Pérez de Guzmán, I., Annihilator alternative algebras. Pacific J. Math. 107 (1983), 8994. 584Google Scholar
Pfitzner, H., L-summands in their biduals have Pełczyński’s property (V). Studia Math. 104 (1993), 91–8. xix, 245, 267Google Scholar
Pfitzner, H., Separable L-embedded Banach spaces are unique preduals. Bull. Lond. Math. Soc. 39 (2007), 1039–44. 241Google Scholar
Pfitzner, H., Phillips’ lemma for L-embedded Banach spaces. Arch. Math. (Basel) 94 (2010), 547–53. 267Google Scholar
Pfitzner, H., A well-known criterion of Pełczyński’s Property (V). Private communication, September 2014. xix, 2, 245, 266, 267Google Scholar
Pfitzner, H., Predual uniqueness coming from the generalized property (X) à la Godefroy–Talagrand. Private communication, April 2017. 238, 241Google Scholar
Phillips, R. S., On symplectic mappings of contraction operators. Studia Math. 31 (1968) 1527. 207Google Scholar
Pinter-Lucke, J., Commutativity conditions for rings: 1950–2005. Expo. Math. 25 (2007), 165–74. 401Google Scholar
Pisier, G., Grothendieck’s theorem for noncommutative C -algebras, with an appendix on Grothendieck’s constants. J. Funct. Anal. 29 (1978), 397415. 342, 343Google Scholar
Pisier, G., Grothendieck’s theorem, past and present. Bull. Amer. Math. Soc. 49 (2012), 237323. xx, 342, 343Google Scholar
Poliquin, R. A. and Zizler, V. E., Optimization of convex functions on w -compact sets. Manuscripta Math. 68 (1990), 249270. 338Google Scholar
Pritchard, F. L., Ideals in the multiplication algebra of a nonassociative K-algebra. Comm. Algebra 21 (1993), 4541–59. 546Google Scholar
Pyatetskii-Shapiro, I. I., On a problem proposed by E. Cartan. Dokl. Akad. Nauk SSSR 124 (1959), 272–3. 210Google Scholar
Pym, J. S., The convolution of functionals on spaces of bounded functions. Proc. London Math. Soc. 15 (1965), 84104. 267Google Scholar
Randrianantoanina, N., Pełczyński’s property (V) for symmetric operator spaces. Proc. Amer. Math. Soc. 125 (1997), 801–6. 267Google Scholar
Robbin, J. W., On the existence theorem for differential equations. Proc. Amer. Math. Soc. 19 (1968), 1005–6. 137Google Scholar
Rodríguez, A., La continuidad del producto de Jordan implica la del ordinario en el caso completo semiprimo. In: Contribuciones en probabilidad, estadística matemática, enseñanza de la matemática y análisis, pp. 280–8, Secretariado de Publicaciones de la Universidad de Granada, Granada, 1979. xxiii, 474Google Scholar
Rodríguez, A., A note on Arens regularity. Quart. J. Math. Oxford 38 (1987), 91–3. 267, 268Google Scholar
Rodríguez, A., On the strong topology of a JBW -triple. Quart. J. Math. Oxford 42 (1991), 99103. xx, 274, 335, 337, 338, 339Google Scholar
Rodríguez, A., Non-associative normed algebras: geometric aspects. In [1189], pp. 299–311. 421, 462Google Scholar
Rodríguez, A., Estructuras de Jordan en Análisis. Rev. Real Acad. Cienc. Exact. Fís. Natur. Madrid 88 (1994), 309–17. 462Google Scholar
Rodríguez, A. and Velasco, M. V., Continuity of homomorphisms and derivations on normed algebras which are tensor products of algebras with involution. Rocky Mountain J. Math. 32 (2002), 1045–55. xxiii, 474, 475Google Scholar
Rodríguez, A. and Villena, A. R., Centroid and extended centroid of JB -algebras, In [734], pp. 223–32. 408Google Scholar
Rosentahl, P. and Soltysiak, A., Formulas for the joint spectral radius of non-commuting Banach algebra elements. Proc. Amer. Math. Soc. 123 (9) (1995), 2705–8. 651Google Scholar
Ruckle, W. H., The infinite sum of closed subspaces of an F-space. Duke Math. J. 31 (1964), 543–54. 584Google Scholar
Runde, V., Review of [462]. MR1706325 (2000f:46067). 596Google Scholar
Russo, B., Derivations and projections on Jordan triples: an introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis. In Advanced courses of mathematical analysis V, pp. 118227, World Sci. Publ., Hackensack, NJ, 2016. 346Google Scholar
Sakai, S., A characterization of W -algebras. Pacific J. Math. 6 (1956), 763–73. 19Google Scholar
Sakai, S., Weakly compact operators on operator algebras. Pacific J. Math. 14 (1964), 659–64. 274, 336Google Scholar
Sakai, S., On topologies of finite W -algebras. Illinois J. Math. 9 (1965), 236–41. 334Google Scholar
Saworotnow, P. P., A generalized Hilbert space. Duke Math. J. 35 (1968), 191–7. 556Google Scholar
Saworotnow, P. P., Trace-class and centralizers of an H -algebra. Proc. Amer. Math. Soc. 26 (1970), 101–4. 550Google Scholar
Saworotnow, P. P. and Friedell, J. C., Trace-class for an arbitrary H -algebra. Proc. Amer. Math. Soc. 26 (1970), 95100. 550Google Scholar
Schafer, R. D., On structurable algebras. J. Algebra 92 (1985), 400–12. 555Google Scholar
Schafer, R. D., Invariant forms on central simple structurable algebras. J. Algebra 122 (1989), 112–7. 556Google Scholar
Schatten, R., The cross-space of linear transformations. Ann. of Math. 47 (1946), 7384. 550Google Scholar
Schatten, R. and von Neumann, J., The cross-space of linear transformations. II. Ann. of Math. 47 (1946), 608–30. 550Google Scholar
Schatten, R. and von Neumann, J., The cross-space of linear transformations. III. Ann. of Math. 49 (1948), 557–82. 550Google Scholar
Sherman, S., Order in operator algebras. Amer. J. Math. 73 (1951), 227–32. 400Google Scholar
Shestakov, I. P., Speciality and deformations of algebras. In: Algebra: Proceedings of the International Algebraic Conference on the Occasion of the 90th Birthday of A. G. Kurosh (Moscow, 1998), pp. 345–56, de Gruyter, Berlin, 2000. xxii, 470Google Scholar
Shulman, V. S., On invariant subspaces of Volterra operators. (Russian) Funk. Anal. i Prilozen 18 (1984), 84–5. xxvi, 651Google Scholar
Shulman, V. S., Invariant subspaces and spectral mapping theorems. In [1189], pp. 313–25. 651Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals. I. Basic properties, tensor products and joint quasinilpotence. In Topological algebras, their applications, and related topics (Ed. by Jarosz, K. and Soltysiak, A.), pp. 293333, Banach Center Publ. 67, Polish Acad. Sci., Warsaw, 2005. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals, II. Applications to spectral theory of multiplication operators. In Elementary operators and their applications (Belfast, 2009) (Ed. by Curto, R. E. and Mathieu, M.), pp. 45114, Oper. Theory Adv. Appl., 212, Birkhäuser/Springer Basel AG, Basel, 2011. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals and the joint spectral radius. (Russian) Funktsional. Anal. i Prilozhen. 46 (2012), 6182; translation in Funct. Anal. Appl. 46 (2012), 287–304. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals, V. From algebra to spectral theory. In Algebraic methods in functional analysis. The Victor Shulman anniversary volume (Ed. by Todorov, I. G. and Turowska, L.), pp. 171280, Oper. Theory Adv. Appl., 233, Birkhäuser/Springer Basel AG, Basel, 2013. 652Google Scholar
Simons, S., On the Dunford–Pettis property and Banach spaces that contain c 0 . Math. Ann. 216 (1975), 225–31. 266Google Scholar
Sinclair, A. M., Homomorphisms from C -algebras. Proc. London Math. Soc. 29 (1974), 435–52. Corrigendum: Proc. London Math. Soc. 32 (1976), 322. 548Google Scholar
Sinclair, A. M. and Tullo, A. W., Noetherian Banach algebras are finite dimensional. Math. Ann. 211 (1974), 151–3. 601Google Scholar
Smirnov, O. N., Simple and semisimple structurable algebras. (Russian) Algebra i Logika 29 (1990), 571–96; translation in Algebra and Logic 29 (1990), 377–94. 555Google Scholar
Smith, J. F., The structure of Hilbert modules. J. London Math. Soc. 8 (1974), 741–9. 556Google Scholar
Smith, R. R. and Ward, J. D., M-ideal structure in Banach algebras. J. Funct. Anal. 27 (1978), 337–49. 19Google Scholar
Soltysiak, A., On the joint spectral radii of commuting Banach algebra elements. Studia Math. 105 (1993), 93–9. 651Google Scholar
Stacey, P. J., Type I 2 JBW-algebras. Quart. J. Math. Oxford 33 (1982), 115–27. 416Google Scholar
Stachó, L. L., A short proof of the fact that biholomorphic automorphisms of the unit ball in certain L p spaces are linear. Acta Sci. Math. (Szeged) 41 (1979), 381–3. 207Google Scholar
Stachó, L. L., On nonlinear projections of vector fields. In Convex analysis and chaos (Sakado, 1998), pp. 4754, Josai Math. Monogr. 1, Josai Univ., Sakado, 1999. 207Google Scholar
Stampfli, J. G., The norm of a derivation. Pacific J. Math. 33 (1970), 737–47. 550Google Scholar
Steptoe, A. C. P., JC -triples and inner ideals in universally reversible JC -algebras. Quart. J. Math. 56 (2005), 397402. 460Google Scholar
Stern, J., Some applications of model theory in Banach space theory. Ann. Math. Logic 9 (1976), 49121. 236Google Scholar
Stone, M. H., Boundedness properties in function-lattices. Canadian J. Math. 1 (1949), 176–86. 421 Google Scholar
Takesaki, M., On the conjugate space of operator algebra. Tôhoku Math. J. 10 (1958), 194203. 334Google Scholar
Taylor, D. C., The strict topology for double centralizer algebras. Trans. Amer. Math. Soc. 150 (1970) 633–43. 400Google Scholar
Tullo, A. W., Conditions on Banach algebras which imply finite dimensionality. Proc. Edinburgh Math. Soc. 20 (1976), 15. 598Google Scholar
Turovskii, Yu. V., Spectral properties of elements of normed algebras, and invariant subspaces. (Russian) Funktsional. Anal. i Prilozhen. 18 (1984), 77–8; translation in Funct. Anal. Appl. 18 (1984), 152–4. 651Google Scholar
Turovskii, Yu. V. and Shulman, V. S., Radicals in Banach algebras, and some problems in the theory of radical Banach algebras. (Russian) Funktsional. Anal. i Prilozhen. 34 (2001), no. 4, 8891; translation in Funct. Anal. Appl. 35 (2001), 312–4. 652Google Scholar
Turovskii, Yu. V. and Shulman, V. S., Topological radicals and the joint spectral radius. (Russian) Funktsional. Anal. i Prilozhen. 46 (2012), 6182; translation in Funct. Anal. Appl. 46 (2012), 287–304. 652Google Scholar
Ülger, A., Weakly compact bilinear forms and Arens regularity. Proc. Amer. Math. Soc. 101 (1987), 697704. 268Google Scholar
Umegaki, H., Weak compactness in an operator space. Kōdai Math. Sem. Rep. 8 (1956), 145–51. 334Google Scholar
Unsain, I., Classification of the simple separable real L -algebras. J. Differential Geometry 7 (1972), 423–51. 554Google Scholar
Upmeier, H., Über die Automorphismengruppen von Banach-Mannigfaltigkeiten mit invarianter Metrik. Math. Ann. 223 (1976), 279–88. 174Google Scholar
Upmeier, H., Remarks on the Campbell–Hausdorff formula for holomorphic vector fields. Private communication, June 2017. xix, 174Google Scholar
Vigué, J.-P., Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. Ann. Sci. École Norm. Sup. (4) 9 (1976), 203–81. xix, 87, 159, 174, 211Google Scholar
Vigué, J.-P., Les domaines bornés symétriques d’un espace de Banach complexe et les systémes triples de Jordan. Math. Ann. 229 (1977), 223–31. 211Google Scholar
Vigué, J.-P., Sur la décomposition d’un domaine borné symétrique en produit continu de domaines bornés symétriques irréductibles. Ann. Sci. École Norm. Sup. (4) 14 (1981), 453–63. 241Google Scholar
Villena, A. R., Continuity of derivations on a complete normed alternative algebra. J. Inst. Math. Comput. Sci. Math. Ser. 3 (1990), 99106. 548Google Scholar
Viola Devapakkiam, C., Hilbert space methods in the theory of Jordan algebras. I. Math. Proc. Cambridge Philos. Soc. 78 (1975), 293300. xxv, 552Google Scholar
Viola Devapakkiam, C. and Rema, P. S., Hilbert space methods in the theory of Jordan algebras. II. Math. Proc. Cambridge Philos. Soc. 79 (1976), 307–19. xxv, 552Google Scholar
Weaver, N., A prime C -algebra that is not primitive. J. Funct. Anal. 203 (2003), 356–61. 467Google Scholar
Wilkins, T. J. D., Spectrum-finite ideals of Jordan-Banach algebras. J. London Math. Soc. 54 (1996), 359–68. 601Google Scholar
Yeadon, F. J., A note on the Mackey topology of a von Neumann algebra. J. Math. Anal. Appl. 45 (1974), 721–2. 336Google Scholar
Yood, B., Closed prime ideals in topological rings. Proc. London Math. Soc. 24 (1972), 307–23. 583, 584Google Scholar
Youngson, M. A., Review of [710]. Bull. Lond. Math. Soc. 44 (2012), 1304–7. xixGoogle Scholar
Zalar, B., Continuity of derivations on Mal’cev H -algebras. Math. Proc. Cambridge Philos. Soc. 110 (1991), 455–9. 548Google Scholar
Zalar, B., On derivations of H -algebras. University of Ljubljana, Preprint Series of the Department of Mathematics, Vol. 29 (1991), 356. 548Google Scholar
Zalar, B., A note on the definition of a nonassociative H -triple. University of Ljubljana, Preprint Series of the Department of Mathematics, Vol. 30 (1992), 361. 561Google Scholar
Zalar, B., Continuity of derivation pairs on alternative and Jordan H -triples. Boll. Un. Mat. Ital. B 7 (1993), 215–30. 559Google Scholar
Zalar, B., Theory of Hilbert triple systems. Yokohama Math. J. 41 (1994), 95126. 558Google Scholar
Zel’manov, E. I., Jordan algebras with finiteness conditions. Algebra Logic 17 (1978), 450–7. 562Google Scholar
Zel’manov, E. I., On prime Jordan algebras. Algebra Logic 18 (1979), 162–75. 364, 437Google Scholar
Zel’manov, E. I., Lie algebras with algebraic associated representation. (Russian) Mat. Sb. (N.S.) 121 ( 163 ) (1983), 545–61; translation in Math. USSR-Sb. 49 (1984), 537–52. 658Google Scholar
Zel’manov, E. I., Primary Jordan triple systems. Sibirsk. Mat. Zh. 24 (1983), 2337. xxii, 437, 438, 459Google Scholar
Zel’manov, E. I., Primary Jordan triple systems. II. Sibirsk. Mat. Zh. 25 (1984), 5061. xxii, 437, 438, 447, 459Google Scholar
Zel’manov, E. I., Lie algebras with a finite grading. Math. USSR Sb. 52 (1985), 347–85. 600Google Scholar
Zel’manov, E. I., On Engel Lie algebras. Soviet Math. Dokl. 35 (1987), 44–7. 658Google Scholar
Zizler, V., On some extremal problems in Banach spaces. Math. Scand. 32 (1973), 214–24. xx, 274, 337Google Scholar
Abraham, R., Marsden, J. E., and Ratiu, T., Manifolds, tensor analysis, and applications. Second edition. Applied Mathematical Sciences, 75. Springer-Verlag, New York, 1988. 135 Google Scholar
Alvermann, K., Normierte nichtkommutative Jordan-Algebren vom Typ I. PhD thesis, Braunschweig 1982. 421 Google Scholar
Behrends, E., M-structure and the Banach–Stone theorem. Lecture Notes in Math. 736, Springer, Berlin, 1979. 350, 351, 398Google Scholar
Bierstedt, K. D., Bonet, J., Maestre, M., and Schmets, J. (eds.), Recent progress in functional analysis. Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, Valencia, Spain, July 3–7, 2000. North Holland Math. Studies 189, Elsevier, Amsterdam 2001. 679, 708Google Scholar
Bonfiglioli, A. and Fulci, R., Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin. Lecture Notes in Math. 2034, Springer, Heidelberg, 2012. 154, 155, 174Google Scholar
Bourbaki, N., Éléments de mathématique: groupes et algèbres de Lie. Chapitres 2 et 3. Springer-Verlag, Berlin, 2006. 154, 155, 174Google Scholar
Cabrera, M., H-álgebras no asociativas reales. H-álgebras de Malcev complejas y reales . PhD thesis, Granada 1987. Tesis Doctorales de la Universidad de Granada, Secretariado de Publicaciones de la Universidad de Granada, 1988. 552, 555Google Scholar
Cartan, H., Sur les groupes de transformations analytiques. Act. Sci. Ind. 198, Hermann, Paris, 1935. 87 Google Scholar
Cartan, H., Cours de calcul différentiel. Second edition. Hermann, Paris, 1977. 53 Google Scholar
Chaperon, M., Calcul différentiel et calcul intégral. Second edition. Dunod, Paris, 2008. 53 Google Scholar
Coleman, R., Calculus on normed vector spaces. Universitext. Springer, New York, 2012. 53, 135, 136Google Scholar
Conway, J. B., Functions of one complex variable. Second edition. Grad. Texts in Math. 11. Springer-Verlag, New York-Berlin, 1978. 44, 55, 58, 101, 185Google Scholar
Dales, H. G., Dashiell, F. K., Jr., Lau, A. T.-M., and Strauss, D., Banach Spaces of Continuous Functions as Dual Spaces. CMS Books Math., Springer, New York, 2016. 421 Google Scholar
Diestel, J., Sequences and series in Banach spaces. Grad. Texts in Math. 92. Springer-Verlag, New York, 1984. 239, 245, 253, 258, 266, 267, 279Google Scholar
Dieudonné, J., Éléments d’analyse. Tome I. Fondements de l’analyse moderne . Third edition. Translated from the English by D. Huet. With a foreword by Gaston Julia. Cahiers Scientifiques XXVIII. Gauthier-Villars, Paris, 1981. 53, 135, 136Google Scholar
Dieudonné, J., Éléments d’analyse . Tome II: Chapitres XII à XV. Cahiers Scientifiques XXXI Gauthier-Villars, Paris, 1968. 335 Google Scholar
Dineen, S., Complex analysis in locally convex spaces. North-Holland Math. Stud. 57. North-Holland Publishing Co., Amsterdam, 1981. 53 Google Scholar
Dineen, S., Complex analysis on infinite-dimensional spaces. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 1999. xxvi, 53Google Scholar
Doran, R. S. and Wichmann, J., Approximate identities and factorization in Banach modules . Lecture Notes in Math. 768, Springer, Berlin, 1979. xxvi, 651, 652Google Scholar
Fernández, A., Teoremas de Wedderburn-Zorn en álgebras alternativas normadas completas, PhD thesis, Universidad de Granada 1983. 583, 584Google Scholar
Fernández, A., Jordan techniques in Lie algebras. Book in progress. 600Google Scholar
Franzoni, T. and Vesentini, E., Holomorphic maps and invariant distances . North-Holland Math. Stud. 69, North-Holland Publishing Co., Amsterdam, 1980. 53, 87Google Scholar
Hervé, M., Analyticity in infinite-dimensional spaces. de Gruyter Studies in Mathematics, 10. Walter de Gruyter & Co., Berlin, 1989. 53 Google Scholar
Horváth, J., Topological vector spaces and distributions. Volume I. Addison-Wesley Publishing Co., Reading, Massachusetts-London-Don Mills, Ontario, 1966. 7, 290Google Scholar
Istrǎtescu, V. I., Inner product structures. Theory and applications. Mathematics and its Applications, 25. D. Reidel Publishing Co., Dordrecht, 1987. 551, 557Google Scholar
Jarchow, H., Locally convex spaces. Mathematische Leitfäden. B. G. Teubner, Stuttgart, 1981. 335 Google Scholar
Johnstone, P. T., Stone spaces. Reprint of the 1982 edition. Cambridge Studies in Advanced Mathematics, 3. Cambridge University Press, Cambridge, 1986. 421 Google Scholar
Jungers, R., The joint spectral radius. Theory and applications. Lecture Notes in Control and Information Sciences, 385. Springer-Verlag, Berlin, 2009. 651 Google Scholar
Kadets, V., Martín, M., Merí, J., and Pérez, A., Spear operators between Banach spaces . Lecture Notes in Math., Springer. 209 Google Scholar
Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vol. II. Advanced theory . Grad. Stud. Math. 16, American Mathematical Society, Providence, RI, 1997. 19 Google Scholar
Kelley, J. L. and Namioka, I., Linear topological spaces. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, NJ, 1963. 288 Google Scholar
Koecher, M., An elementary approach to bounded symmetric domains, Lecture Notes (Rice University, Houston, TX, 1969). 211 Google Scholar
Lang, S., Differential and Riemannian manifolds . Third edition. Grad. Texts in Math. 160. Springer-Verlag, New York, 1995. 135 Google Scholar
Lee, J. M., Introduction to smooth manifolds . Second Edition. Grad. Texts in Math. 218. Springer, New York, 2013. 135 Google Scholar
Lelong-Ferrand, J. and Arnaudiès, J. M., Cours de mathématiques. Tome 2: Analyse . Fourth edition. Dunod, Paris, 1977. 53 Google Scholar
Mellon, P., An introduction to bounded symmetric domains . Textos de Matemática. Série B. Universidade de Coimbra, Departamento de Matemática, Coimbra, 2000. 210, 211Google Scholar
Moreno, A., Álgebras de Jordan-Banach primitivas, PhD thesis, Universidad de Granada 1995. 470 Google Scholar
Mujica, J., Complex analysis in Banach spaces . Dover Publications, Inc. Mineola, New York, 2010. 53, 87Google Scholar
Narasimhan, R., Several complex variables . Chicago Lectures in Mathematics. The University of Chicago Press, Chicago and London, 1971. 87, 207Google Scholar
Neher, E., Jordan triple systems by the grid approach. Lecture Notes in Math. 1280, Springer-Verlag, Berlin, 1987. 557 Google Scholar
Pedersen, G. K., C-algebras and their automorphism groups. London Math. Soc. Monogr. 14, Academic Press, London-New York, 1979. 408 Google Scholar
Pérez de Guzmán, I., Álgebras alternativas normadas. Teorema de estructura para H-álgebras alternativas . PhD thesis, Granada 1977. Tesis Doctorales de la Universidad de Granada 266, Secretariado de Publicaciones de la Universidad de Granada, 1980. 549 Google Scholar
Reich, S. and Shoikhet, D., Nonlinear semigroups, fixed points, and geometry of domains in Banach spaces. Imperial College Press, London, 2005. 79, 87, 88, 135Google Scholar
Reutenauer, C., Free Lie algebras. London Mathematical Society Monographs. New Series, 7. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993. 154, 174Google Scholar
Ringrose, J. R., Compact non-self-adjoint operators. Van Nostrand Reinhold Co., London, 1971. 481, 524Google Scholar
Saitô, K. and Wright, J. D. M., Monotone complete C-algebras and generic dynamics. Springer Monographs in Mathematics. Springer, London, 2015. 19 Google Scholar
Singer, I., Bases in Banach spaces . I. Die Grundlehren der mathematischen Wissenschaften, Band 154. Springer-Verlag, New York-Berlin, 1970. 239 Google Scholar
Takesaki, M., Theory of operator algebras. I. Reprint of the first (1979) edition. Encyclopaedia of Mathematical Sciences, 124. Operator Algebras and Noncommutative Geometry, 5. Springer-Verlag, Berlin, 2002. 332, 334, 335Google Scholar
Upmeier, H., Über die Automorphismengruppen beschränkter Gebiete in Banachräumen. PhD thesis, Tübingen 1975. 174 Google Scholar
Vigué, J.-P., Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. PhD thesis, Publication Mathématique d’Orsay, 1976. 87, 135, 174, 211Google Scholar
Willard, S., General topology. Reprint of the 1970 original [Addison-Wesley, Reading, MA; MR0264581]. Dover Publications, Inc., Mineola, NY, 2004. 87, 280Google Scholar
Zemánek, J. (Editor), Functional analysis and operator theory (Warsaw, 1992). Banach Center Publ., 30, Polish Acad. Sci., Warsaw, 1994. 665, 707, 709Google Scholar
Aarnes, J. F., On the Mackey-topology for a von Neumann algebra. Math. Scand . 22 (1968), 87107. 332Google Scholar
Acosta, M. D., An inequality for norm of operators. Extracta Math . 10 (1995), 115–8. 469Google Scholar
Acosta, M. D., Denseness of norm attaining mappings. RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat . 100 (2006), 930. 338Google Scholar
Akemann, C. A., The dual space of an operator algebra. Trans. Amer. Math. Soc . 126 (1967), 286302. xx, 268, 274, 332, 334, 335Google Scholar
Albert, A. A., A theory of trace-admissible algebras. Proc. Nat. Acad. Sci. USA 35 (1949), 317–22. Reprinted in [692], pp. 491–6. 545Google Scholar
Albert, A. A. and Jacobson, N., On reduced exceptional simple Jordan algebras. Ann. of Math . 66 (1957), 400–17. Reprinted in [692], pp. 677–94. 361Google Scholar
Albrecht, E. and Dales, H. G., Continuity of homomorphisms from C∗-algebras and other Banach algebras. In Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981), pp. 375–96, Lecture Notes in Math. 975, Springer, Berlin-New York, 1983. 549Google Scholar
Alfsen, E. M. and Effros, E. G., Structure in real Banach spaces. I, II. Ann. of Math . 96 (1972), 98128; ibid. 96 (1972), 129–73. 19, 398Google Scholar
Allison, B. N., A class of nonassociative algebras with involution containing the class of Jordan algebras. Math. Ann . 237 (1978), 133–56. 555Google Scholar
Allison, B. N., Models of isotropic simple Lie algebras. Comm. Algebra 7 (1979), 1835–75. 555Google Scholar
Allison, B. N. and Faulkner, J. R., The algebra of symmetric octonion tensors. Nova J. Algebra Geom . 2 (1993), 4757. 555Google Scholar
Anquela, J. A., Cabrera, M., and Moreno, A., Eater ideals in Jordan algebras. J. Pure Appl. Algebra 125 (1998), 117. 464Google Scholar
Ara, P., The extended centroid of C -algebras. Archiv. Math . 54 (1990), 358–64. 408Google Scholar
Ara, P., On the symmetric algebra of quotients of a C -algebra. Glasgow Math. J. 32 (1990), 377–9. 408Google Scholar
Arazy, J., An application of infinite-dimensional holomorphy to the geometry of Banach spaces. In Geometrical aspects of functional analysis (1985/86), pp. 122–50, Lecture Notes in Math. 1267, Springer, Berlin, 1987. xix, 87, 135, 174, 207Google Scholar
Arens, R. and Goldberg, G., Quadrative seminorms and Jordan structures on algebras. Linear Algebra Appl . 181 (1993), 269–78. 470Google Scholar
Aupetit, B., Analytic multivalued functions in Banach algebras and uniform algebras. Adv. Math . 44 (1982), 1860. 603Google Scholar
Aupetit, B., Some uses of subharmonicity in functional analysis. In Spectral theory (Warsaw, 1977), pp. 31–7, Banach Center Publ. 8, Polish Acad. Sci. Inst. Math., Warsaw, 1982. 603Google Scholar
Aupetit, B., Inessential elements in Banach algebras. Bull. London Math. Soc . 18 (1986), 493–7. 599Google Scholar
Aupetit, B., Spectral characterization of the radical in Banach and Jordan-Banach algebras. Math. Proc. Cambridge Philos. Soc . 114 (1993), 31–5. 603Google Scholar
Aupetit, B., Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras. J. London Math. Soc . 62 (2000), 917–24. 603Google Scholar
Aupetit, B. and Mouton, H. du T., Trace and determinant in Banach algebras. Studia Math . 121 (1996), 115–36. 601Google Scholar
Aupetit, B. and Zraïbi, A., Propriétés analytiques du spectre dans les algèbres de Jordan-Banach. Manuscripta Math . 38 (1982), 381–6. 596, 597Google Scholar
Bachelis, G. F., Homomorphisms of annihilator Banach algebras. Pacific J. Math . 25 (1968), 229–47. xxv, 584Google Scholar
Bade, W. G., Curtis, P. C. JR., and Sinclair, A. M., Raising bounded groups and splitting of radical extensions of conmmutative Banach algebras. Studia Math . 141 (1) (2000), 8598. 651Google Scholar
Baker, J. W. and Pym, J. S., A remark on continuous bilinear mappings. Proc. Edinburgh Math. Soc . 17 (1970/71), 245–8. 436Google Scholar
Bakić, D. and Guljaš, B., Operators on Hilbert H -modules. J. Operator Theory 46 (2001), 123–37. 557Google Scholar
Balachandran, V. K., Automorphisms of L -algebras. Tôhoku Math. J . 22 (1970), 163–73. 549Google Scholar
Balachandran, V. K., Real L -algebras. Indian J. Pure Appl. Math . 3 (1972), 1224–46. 554Google Scholar
Barton, T. J., Dang, T., and Horn, G., Normal representations of Banach Jordan triple systems. Proc. Amer. Math. Soc . 102 (1988), 551–5. 211, 241Google Scholar
Barton, T. J. and Friedman, Y., Grothendieck’s inequality for JB -triples and applications. J. London Math. Soc . 36 (1987), 513–23. xx, 268, 274, 275, 337, 338, 345, 346Google Scholar
Barton, T. J. and Timoney, R. M., Weak∗-continuity of Jordan triple products and its applications. Math. Scand . 59 (1986), 177–91. xix, 2, 211, 236, 237Google Scholar
Beidar, K. I., Mikhalev, A. V., and Slinko, A. M., A criterion for primeness of nondegenerate alternative and Jordan algebras. Trudy Moskov. Mat. Obshch . 50 (1987), 130–7; translation in Trans. Moscow Math. Soc. 50 (1988), 129–37. xxii, 408, 468Google Scholar
Benkart, G., On inner ideals and ad-nilpotent elements of Lie algebras. Trans. Amer. Math. Soc . 232 (1977), 6181. 600Google Scholar
Benslimane, M. and Boudi, N., Isomorphisms of Jordan-Banach algebras. Extracta Math . 11 (1996), 414–6. 603Google Scholar
Benslimane, M. and Boudi, N., Ring isomorphisms of Jordan-Banach algebras. In Commutative ring theory (Fès, 1995), pp. 105–11, Lect. Notes Pure Appl. Math. 185, Dekker, New York, 1997. 603Google Scholar
Benslimane, M. and Mesmoudi, L., Characterization of commutative normed algebras. In [705], pp. 53–7. 436Google Scholar
Benslimane, M., Mesmoudi, L., and Rodríguez, A., A characterization of commutativity for non-associative normed algebras. Extracta Math . 15 (2000), 121–43. xxii, 436Google Scholar
Berger, M. A. and Wang, Y., Bounded semigroups of matrices. Linear Algebra Appl . 166 (1992), 21–7. 651Google Scholar
Blecher, D. P. and Paulsen, V. I., Multipliers of operator spaces, and the injective envelope. Pacific J. Math . 200 (2001), 117. 273Google Scholar
Bombal, F., On (V) sets and Pełczyński’s property (V). Glasgow Math. J. 32 (1990), 109–20. 266Google Scholar
Bonsall, F. F. and Goldie, A. W., Annihilator algebras. Proc. London Math. Soc . 4 (1954), 154–67. 584Google Scholar
Boudi, N., Marhnine, H., and Zarhouti, C., Additive derivations on Jordan Banach pairs. Comm. Algebra 32 (2004), 3609–25. 466, 603Google Scholar
Boyadjiev, H. N. and Youngson, M. A., Alternators on Banach Jordan algebras. C. R. Acad. Bulgare Sci . 33 (1980), 1589–90. 400Google Scholar
Braun, R., Kaup, W., and Upmeier, H., On the automorphisms of circular and Reinhardt domains in complex Banach spaces. Manuscripta Math . 25 (1978), 97133. 207Google Scholar
Brešar, M., Functional identities: A survey. Contemp. Math . 259 (2000), 93109. 602Google Scholar
Brešar, M. and Villena, A. R., The range of a derivation on a Jordan-Banach algebra. Studia Math . 146 (2001), 177200. 466, 707Google Scholar
Bunce, L. J., The theory and structure of dual JB-algebras. Math. Z. 180 (1982), 525–34. 584, 598Google Scholar
Bunce, L. J., On compact action in JB-algebras. Proc. Edinburgh Math. Soc . 26 (1983), 353–60. 400Google Scholar
Bunce, L. J., Norm preserving extensions in JBW -triple preduals. Quart. J. Math. Oxford 52 (2001), 133–6. 338, 339, 346Google Scholar
Bunce, L. J. and Chu, C.-H., Compact operations, multipliers and Radon-Nikodym property in JB -triples. Pacific J. Math . 153 (1992), 249–65. xx, 275, 346, 450, 459, 461Google Scholar
Bunce, L. J. and Chu, C.-H., Real contractive projections on commutative C -algebras. Math. Z . 226 (1997), 85101. 210Google Scholar
Bunce, L. J., Chu, C.-H., Stachó, L. L., and Zalar, B., On prime JB -triples. Quart. J. Math. Oxford 49 (1998), 279–90. 409Google Scholar
Cabello, J. C. and Cabrera, M., Structure theory for multiplicatively semiprime algebras. J. Algebra 282 (2004), 386421. xxv, 546, 584Google Scholar
Cabello, J. C., Cabrera, M., and Fernández, A., π-complemented algebras through pseudocomplemented lattices. Order 29 (2012), 463–79. 585Google Scholar
Cabello, J. C., Cabrera, M., López, G., and Martindale, W. S. III, Multiplicative semiprimeness of skew Lie algebras. Comm. Algebra 32 (2004), 3487–501. 546Google Scholar
Cabello, J. C., Cabrera, M., and Nieto, E., ε-complemented algebras. J. Algebra 349 (2012), 234–67. 546, 585Google Scholar
Cabello, J. C., Cabrera, M., Rodríguez, A., and Roura, R., A characterization of π-complemented algebras. Comm. Algebra 41 (2013), 3067–79. 585Google Scholar
Cabello, J. C., Cabrera, M., and Roura, R., A note on the multiplicative primeness of degenerate Jordan algebras. Sib. Math. J . 51 (2010), 818–23. 546Google Scholar
Cabello, J. C., Cabrera, M., and Roura, R., π-complementation in the unitisation and multiplication algebras of a semiprime algebra. Comm. Algebra 40 (2012), 3507–31. 546Google Scholar
Cabrera, M., El Marrakchi, A., Martínez, J., and Rodríguez, A.. Bounded differential operators on Hilbert modules and derivations of structurable H -algebras. Comm. Algebra 21 (1993), 2905–45. 559Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Hilbert modules over H -algebras in relation with Hilbert ternary rings. In [734], pp. 33–44. 558Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Hilbert modules revisited: orthonormal bases and Hilbert–Schmidt operators. Glasgow Math. J . 37 (1995), 4554. 557Google Scholar
Cabrera, M. and Mohammed, A. A., Extended centroid and central closure of the multiplication algebra. Comm. Algebra 27 (1999), 5723–36. 546, 576Google Scholar
Cabrera, M. and Mohammed, A. A., A representation theorem for algebras with commuting involutions. Linear Algebra Appl . 306 (2000), 2531. 476Google Scholar
Cabrera, M. and Mohammed, A. A., Extended centroid and central closure of multiplicatively semiprime algebras. Comm. Algebra 29 (2001), 1215–33. 546Google Scholar
Cabrera, M. and Mohammed, A. A., Totally multiplicatively prime algebras. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 1145–62. xxiii, 408, 546, 547, 549Google Scholar
Cabrera, M. and Mohammed, A. A., Algebra of quotients with bounded evaluation of a normed prime algebra. In: Operator theory and Banach algebras. Proceedings of the International Conference in Analysis, Rabat (Moroco), April 12–14, 1999 (eds. Chidami, M., Curto, R., Mbekhta, M., Vasilescu, F.-H. and Zemánek, J.). Theta Found., Bucharest, 2003, pp. 3950. 547Google Scholar
Cabrera, M. and Mohammed, A. A., Algebras of quotients with bounded evaluation of a normed semiprime algebra. Studia Math . 154 (2003), 113–35. 547Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., On primitive Jordan-Banach algebras. In [733], pp. 54–9. 463Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., On the behaviour of Jordan-algebra norms on associative algebras. Studia Math . 113 (1995), 81100. xxii, 469, 470, 471, 474Google Scholar
Cabrera, M. and Rodríguez, A., A characterization of the centre of a nondegenerate Jordan algebra. Comm. Algebra 21 (1993), 359–69. 469Google Scholar
Cabrera, M. and Rodríguez, A., Zel’manov’s theorem for nondegenerately ultraprime Jordan-Banach algebras. In [733], pp. 60–5. 462Google Scholar
Cabrera, M. and Villena, A. R., Multiplicative-semiprimeness of nondegenerate Jordan algebras. Comm. Algebra 32 (2004), 39954003. 546Google Scholar
Cao, P. and Turovskii, Yu. V., Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras. Studia Math . 235 (2016), 171208. 603, 652Google Scholar
Cartan, É., Sur les domaines bornes homogenes de l’espace de n variables complexes. Abh. Math. Sem. Univ. Hamburg 11 (1935), 116–62. 210Google Scholar
Cartan, H., Les fonctions de deux variables complexes et le problème de la représentation analytique. J. Math. Pures Appl ., 9 e série, 10 (1931), 1114. 87Google Scholar
Castellón, A. and Cuenca, J. A., Compatibility in Jordan H -triple systems. Boll. Un. Mat. Ital. B 4 (1990), 433–47. 560Google Scholar
Castellón, A. and Cuenca, J. A., Alternative H -triple systems. Comm. Algebra 20 (1992), 3191–206. 561Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Ternary H -algebras. Boll. Un. Mat. Ital. B 6 (1992), 217–28. 559Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Jordan H -triples. In [733], pp. 66–72. 549, 560Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Special Jordan H -triple system. Comm. Algebra 28 (2000), 4699–706. 560Google Scholar
Chaperon, M., On the Cauchy–Kowalevski theorem. Enseign. Math . 55 (2009), 359–71. 137Google Scholar
Chu, C.-H. and Iochum, B., Weakly compact operators on Jordan triples. Math. Ann . 281 (1988), 451–8. 335, 340, 341Google Scholar
Chu, C.-H. and Iochum, B., Complementation of Jordan triples in von Neumann algebras. Proc. Amer. Math. Soc . 108 (1990), 1924. 336Google Scholar
Chu, C.-H., Moreno, A., and Rodríguez, A., On prime real JB -triples. In Function spaces (Edwardsville, IL, 1998), pp. 105–9, Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999. 346Google Scholar
Cohen, P. J., Factorization in group algebras. Duke Math. J . 26 (1959), 199205. 659Google Scholar
Crabb, M. J., A new prime C -algebra that is not primitive. J. Funct. Anal . 236 (2006), 630–3. 467Google Scholar
Cuenca, J. A., Sur la théorie de structure des H -algèbres de Jordan non commutatives. In [749], pp. 143–52. 553Google Scholar
Cuenca, J. A., Moufang H -algebras. Extracta Math . 17 (2002), 239–46. 552Google Scholar
Cuenca, J. A., García, A., and Martín, C., Jacobson density for associative pairs and its applications. Comm. Algebra 17 (1989), 2595–610. 560Google Scholar
Cuenca, J. A., García, A., and Martín, C., Prime associative superalgebras with nonzero socle. Algebras Groups Geom . 11 (1994), 359–69. 560Google Scholar
Cuenca, J. A. and Martín, C., Jordan two-graded H -algebras. In [734], pp. 91–100. 559, 560Google Scholar
Cuenca, J. A. and Miguel, F., On a Hopf’s theorem. Preprint 2016. 409Google Scholar
Cuenca, J. A. and Sánchez, A., Structure theory for real noncommutative Jordan H -algebras. J. Algebra 164 (1994), 481–99. 553Google Scholar
Cuntz, J., On the continuity of semi-norms on operator algebras. Math. Ann . 220 (1976), 171–83. 399Google Scholar
Curto, R. E., Spectral theory of elementary operators. In Elementary operators and applications (Blaubeuren, 1991) (Ed. by Mathieu, M.), pp. 352, World Sci. Publ., River Edge, NJ, 1992. 635Google Scholar
D’Amour, A., Quadratic Jordan systems of Hermitian type. J. Algebra 149 (1992), 197233. xxii, 438, 448, 459, 461Google Scholar
D’Amour, A. and McCrimmon, K., The structure of quadratic Jordan systems of Clifford type. J. Algebra 234 (2000), 3189. xxii, 438, 452, 453, 454, 459Google Scholar
Dieudonné, J., Sur le socle d’un anneau et les anneaux simples infinis. Bull. Soc. Math. France 70 (1942), 4675. 598Google Scholar
Dineen, S., Complete holomorphic vector fields on the second dual of a Banach space. Math. Scand . 59 (1986), 131–42. 236Google Scholar
Dineen, S. and Timoney, R. M., The centroid of a JB -triple system. Math. Scand . 62 (1988), 327–42. 346Google Scholar
Dineen, S. and Timoney, R. M., The algebraic metric of Harris on JB -triple systems. Proc. Roy. Irish Acad. Sect. A 90 (1990), 8397. 558Google Scholar
Dixmier, J., Sur les C -algèbres. Bull. Soc. Math. France 88 (1960), 95112. 467Google Scholar
Dixon, P. G., Topologically nilpotent Banach algebras and factorization. Proc. Roy. Soc. Edinburgh Sect A 119 (1991), 329–41. xxvi, 650, 651, 654, 655, 657Google Scholar
Dixon, P. G. and Müller, V., A note on topologically nilpotent Banach algebras. Studia Math . 102 (1992), 269–75. xxvi, 623, 650, 651, 653Google Scholar
Dixon, P. G. and Willis, G. A., Approximate identities in extensions of topologically nilpotent Banach algebras. Proc. Roy. Soc. Edinburgh 122A (1992), 4552. xxvi, 650, 651Google Scholar
Doran, R. S. and Wichmann, J., The Gelfand–Naimark theorems for C -algebras. Enseignement Math . 23 (1977), 153–80. xviiGoogle Scholar
Draper, C., Fernández, A., García, E., and Gómez, M., The socle of a nondegenerate Lie algebra. J. Algebra 319 (2008), 2372–94. 600Google Scholar
Edgar, G. A., An ordering for the Banach spaces. Pacific J. Math . 108 (1983), 8398. 266Google Scholar
Edwards, C. M. and Rüttimann, G. T., A characterization of inner ideals in JB -triples. Proc. Amer. Math. Soc . 116 (1992), 1049–57. 339Google Scholar
El Kinani, A. and Oudadess, M., Un critère généralisé de Le Page et commutativité. C. R. Math. Rep. Acad. Sci. Canada 18 (1996), 71–4. 436Google Scholar
El Marrakchi, A., Sur l’unité approchée des H∗-algèbres structurables avec annulateur zéro. Int. J. Math. Game Theory Algebra 13 (2003), 267–79. 556Google Scholar
Elsner, L., The generalized spectral-radius theorem: an analytic-geometric proof. Linear Algebra Appl . 220 (1995), 151–9. 651Google Scholar
Emmanuele, G., On the Banach spaces with the property (V ) of Pełczyński. Ann. Mat. Pura Appl . 152 (1988), 171–81. 266Google Scholar
Essaleh, A. B. A., Peralta, A. M., and Ramírez, M. I., Pointwise-generalized-inverses of linear maps between C -algebras and JB -triples. Operators and Matrices (to appear). 273, 274Google Scholar
Fernández, A., Banach-Jordan pair. In [741], pp. 57–8. 462, 600Google Scholar
Fernández, A., A Jordan approach to finitary Lie algebras. Quart. J. Math . 67 (2016), 565–71. 600Google Scholar
Fernández, A. and García, E., Algebraic lattices and nonassociative structure. Proc. Amer. Math. Soc . 126 (1998), 3211–21. 584Google Scholar
Fernández, A., García, E., and Gómez, M., The Jordan algebras of a Lie algebra. J. Algebra 308 (2007), 164–77. 600Google Scholar
Fernández, A., García, E., Sánchez, E., and Siles, M., Strong regularity and Hermitian Hilbert triples. Quart. J. Math. Oxford 45 (1994), 4355. 558Google Scholar
Fernández, A. and Golubkov, A. Yu., Lie algebras with an algebraic adjoint representation revisited. Manuscripta Math . 140 (2013), 363–76. 600Google Scholar
Fernández, A., Marhnine, H., and Zarhouti, C., Derivations on Banach-Jordan pairs. Quart. J. Math. Oxford 52 (2001), 269–83. 466, 603Google Scholar
Fernández, A. and Tocón, M. I., Pseudocomplemented semilatices, boolean algebras, and compatible products. J. Algebra 242 (2001), 6091. 584Google Scholar
Fernández, A. and Tocón, M. I., Strongly prime Jordan pairs with nonzero socle. Manuscripta Math . 111 (2003), 321–40. 600Google Scholar
Fernández-Polo, F. J., Garcés, J. J., Peralta, A. M., and Villanueva, I., Tingley’s problem for spaces of trace class operators. Linear Algebra Appl . 529 (2017), 294323. 550Google Scholar
Filippov, V. T., On the theory of Mal’cev algebras. Algebra i Logika 16 (1977), 101–8. 555Google Scholar
Finston, D., On multiplication algebras. Trans. Amer. Math. Soc . 293 (1986), 807–18. 546Google Scholar
Friedman, Y. and Russo, B., Contractive projections on operator triple systems. Math. Scand . 52 (1983), 279311. 210, 331Google Scholar
Garimella, R. V., On continuity of derivations and epimorphisms on some vector-valued group algebras. Bull. Austral. Math. Soc . 56 (1997), 209–15. 596Google Scholar
Giellis, G. R., A characterization of Hilbert modules. Proc. Amer. Math. Soc . 36 (1972), 440–2. 556Google Scholar
Godefroy, G., Épluchabilité et unicité du prédual. Séminaire Choquet, 17e année (1977/78), Initiation á l’analyse, Fasc. 2, Comm. No. 11, 3 pp., Secrétariat Math., Paris, 1978. 8 Google Scholar
Godefroy, G., Parties admissibles d’un espace de Banach. Applications. Ann. Sci. École Norm. Sup. (4) 16 (1983), 109–22. 237, 267Google Scholar
Godefroy, G., Existence and uniqueness of isometric preduals: a survey. In Banach space theory (Iowa City, IA, 1987) (Ed. by Lin, B.-L.), pp. 131–93, Contemp. Math., 85, Amer. Math. Soc., Providence, 1989. 238, 241Google Scholar
Godefroy, G. and Iochum, B., Arens-regularity of Banach algebras and the geometry of Banach spaces. J. Funct. Anal . 80 (1988), 4759. xix, 245, 267, 421Google Scholar
Godefroy, G. and Saab, P., Quelques espaces de Banach ayant les propriétés (V) ou (V ) de A. Pełczyński. C. R. Acad. Sci. Paris Sér. I Math . 303 (1986), 503–6. 245, 266Google Scholar
Godefroy, G. and Saab, P., Weakly unconditionally convergent series in M-ideals. Math. Scand . 64 (1989), 307–18. 266Google Scholar
Godefroy, G. and Talagrand, M., Classes d’espaces de Banach à prédual unique. C. R. Acad. Sci. Paris Sér. I Math . 292 (1981), 323–5. 238Google Scholar
Godefroy, G. and Talagrand, M., Nouvelles classes d’espaces de Banach à prédual unique. Séminaire d’Analyse Fonctionnelle de l’École Polytechnique, 1980/81. 238, 239, 240, 241Google Scholar
Gorin, E. A. and Lin, V. Ja., A condition on the radical of a Banach algebra guaranteeing strong decomposability. (Russian) Mat. Zametki 2 (1967), 589–592; translation in Mathematical Notes 2 (1967), 851–2. 651Google Scholar
Grabiner, S., Finitely generated, Noetherian, and Artinian Banach modules. Indiana Univ. Math. J . 26 (1977), 413–25. 601Google Scholar
Grothendieck, A., Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8 (1953), 179. Reprinted in Resenhas 2 (1996), 401–80. xx, 275, 342, 343Google Scholar
Grothendieck, A., Sur les applications linéaires faiblement compactes d’espaces du type C(K). Canadian J. Math . 5 (1953), 129–73. 334Google Scholar
Gulick, S. L., Commutativity and ideals in the biduals of topological algebras. Pacific J. Math . 18 (1966), 121–37. 268Google Scholar
Haagerup, U., Solution of the similarity problem for cyclic representations of C∗-algebras. Ann. Math . 118 (1983), 215–40. 342Google Scholar
Haagerup, U., The Grothendieck inequality for bilinear forms on C -algebras. Adv. in Math . 56 (1985), 93116. 343, 344Google Scholar
Haagerup, U. and Hanche-Olsen, H., Tomita–Takesaki theory for Jordan algebras. J. Operator Theory 11 (1984), 343–64. 339Google Scholar
Haagerup, U. and Itoh, T., Grothendieck type norms for bilinear forms on C -algebras. J. Operator Theory 34 (1995), 263–83. 342Google Scholar
de la Harpe, P., Classification des L -algèbres semi-simples réelles séparables. C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A1559–61. 554Google Scholar
Harris, L. A., Schwarz’s lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A . 62 (1969), 1014–7. 207Google Scholar
Harris, L. A., A continuous form of Schwarz’s lemma in normed linear spaces. Pacific J. Math . 38 (1971), 635–9. 207Google Scholar
Harris, L. A., Analytic invariants and the Schwarz–Pick inequality. Israel J. Math . 34 (1979), 177–97. 558Google Scholar
Harris, L. A., A generalization of C -algebras. Proc. London Math. Soc . 42 (1981), 331–61. 459Google Scholar
Henriksen, M., A simple characterization of commutative rings without maximal ideals. Amer. Math. Monthly 82 (1975), 502–5. 659Google Scholar
Henson, C. W. and Moore, L. C., Jr., Subspaces of the nonstandard hull of a normed space. Trans. Amer. Math. Soc . 197 (1974), 131–43. 236Google Scholar
Hessenberger, G., Analytic properties of the spectrum in Banach Jordan systems. Collect. Math . 47 (1996), 277–84. 603Google Scholar
Horn, G., Characterization of the predual and ideal structure of a JBW -triple. Math. Scand . 61 (1987), 117–33. xix, 2, 211, 237, 238, 239, 241Google Scholar
Horn, G. and Neher, E., Classification of continuous JBW -triples. Trans. Amer. Math. Soc . 306 (1988), 553–78. 340, 344, 459Google Scholar
Jacobson, N., A note on non-associative algebras. Duke Math. J . 3 (1937), 544–8. 545Google Scholar
James, R. C., Uniformly non-square Banach spaces. Ann. of Math . 80 (1964), 542–50. 261Google Scholar
Jamjoom, F. B., Peralta, A. M., and Siddiqui, A. A., Jordan weak amenability and orthogonal forms on JB -algebras. Banach J. Math. Anal . 9 (2015), 126–45. 346Google Scholar
Jamjoom, F. B., Peralta, A. M., Siddiqui, A. A., and Tahlawi, H. M., Approximation and convex decomposition by extremals and the λ-function in JBW -triples. Quart. J. Math. Oxford 66 (2015), 583603. 346Google Scholar
Jarchow, H., Weakly compact operators on C(K) and C -algebras. In Functional analysis and its applications (Nice, 1986) (Ed. by Hogbe-Nlend, H.), pp. 263–99, ICPAM Lecture Notes, World Sci. Publishing, Singapore, 1988. 274, 335Google Scholar
Jeang, J.-S. and Ko, C.-C., On the commutativity of C -algebras. Manuscripta Math . 115 (2004), 195–8. 401Google Scholar
Ji, G. and Tomiyama, J., On characterizations of commutativity of C -algebras. Proc. Amer. Math. Soc . 131 (2003), 3845–9. 401Google Scholar
Johnson, W. B., Rosenthal, H. P., and Zippin, M., On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math . 9 (1971), 488506. 236Google Scholar
Kadison, R. V., Operator algebras with a faithful weakly-closed representation. Ann. of Math . 64 (1956), 175–81. 19Google Scholar
Kalton, N. J., Rademacher series and decoupling. New York J. Math . 11 (2005), 563–95. 343Google Scholar
Kantrowitz, R. and Neumann, M. M., Automatic continuity of homomorphisms and derivations on algebras of continuous vector-valued functions. Czechoslovak Math. J . 45 ( 120 ) (1995), 747–56. 596Google Scholar
Kaplansky, I., Regular Banach algebras. J. Indian Math. Soc . 12, (1948), 5762. 597Google Scholar
Kaup, W., Jordan algebras and holomorphy. In Functional analysis, holomorphy, and approximation theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978) (Ed. by Machado, S.), pp. 341–65, Lecture Notes in Math., 843, Springer, Berlin, 1981. 211Google Scholar
Kaup, W., Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension. I. Math. Ann . 257 (1981), 463–86. II Math. Ann. 262 (1983), 57–75. 211, 557Google Scholar
Kaup, W., Hermitian Jordan triple systems and the automorphisms of bounded symmetric domains. In [733], pp. 204–14. 210Google Scholar
Kaup, W., On spectral and singular values in JB -triples. Proc. Roy. Irish Acad. Sect. A 96 (1996), 95103. 210Google Scholar
Kaup, W. and Upmeier, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc. Amer. Math. Soc . 58 (1976), 129–33. 207Google Scholar
Kissin, E., Shulman, V. S., and Turovskii, Yu. V., Topological radicals and Frattini theory of Banach Lie algebras. Integral Equations Operator Theory 74 (2012), 51121. 652Google Scholar
Le Page, C., Sur quelques conditions entraînant la commutativité dans les algèbres de Banach. C. R. Acad. Sci. Paris Sér. A–B 265 (1967), A235A237. xxii, 347, 423, 436Google Scholar
Lin, C. S., On commutativity of C -algebras. Glasgow Math. J . 29 (1987), 93–7. 400Google Scholar
Lindenstrauss, J., On operators which attain their norm. Israel J. Math . 1 (1963), 139148. xx, 274, 337, 338Google Scholar
Lindenstrauss, J. and Rosenthal, H. P., The L p -spaces. Israel J. Math . 7 (1969), 325–49. 236Google Scholar
Loos, O., On the socle of a Jordan pair. Collect. Math . 40 (1989), 109–25. 599, 601Google Scholar
Loos, O., Finiteness conditions in Jordan pairs. Math. Z . 206 (1991), 577–87. 558Google Scholar
Loos, O. and Neher, E., Complementation of inner ideals in Jordan pairs. J. Algebra 166 (1994), 255–95. 601Google Scholar
Mackey, M. and Mellon, P., A Schwarz lemma and composition operators. Integral Equations Operator Theory 48 (2004), 511–24. 210Google Scholar
Maouche, A., Extension d’un théorème de Harte et applications aux algèbres de Jordan-Banach. Monatsh. Math . 122 (1996), 205–13. 603Google Scholar
Maouche, A., Diagonalization in Banach algebras and Jordan-Banach algebras. Extracta Math . 19 (2004), 257–60. 603Google Scholar
Martín, M., Norm-attaining compact operators. J. Funct. Anal . 267 (2014), 1585–92. 338Google Scholar
Martínez, J., Derivations of structurable H -algebras. In: Nonassociative algebra and its applications (São Paulo, 1998), pp. 219–27, Lecture Notes in Pure and Appl. Math. 211, Dekker, New York, 2000. 559Google Scholar
Mathieu, M., Weakly compact homomorphisms from C -algebras are of finite rank. Proc. Amer. Math. Soc . 107 (1989), 761–2. 336Google Scholar
Mathieu, M., Elementary operators on prime C -algebras, I. Math. Ann . 284 (1989), 223–44. xxi, 408Google Scholar
Mathieu, M., The symmetric algebra of quotients of an ultraprime Banach algebra. J. Austral. Math. Soc. Ser. A 50 (1991), 7587. 468, 469, 547Google Scholar
Mathieu, M., Review of [869]. MR1853520 (2002k:46123). 466Google Scholar
Mathieu, M. and Runde, V., Derivations mapping into the radical. II. Bull. London Math. Soc . 24 (1992), 485–7. 466Google Scholar
McCrimmon, K., On Herstein’s theorems relating Jordan and associative algebras. J. Algebra 13 (1969), 382–92. 367Google Scholar
McCrimmon, K., A characterization of the radical of a Jordan algebra. J. Algebra 18 (1971), 103–11. 597Google Scholar
McCrimmon, K., The Zel’manov approach to Jordan homomorphisms of associative algebras. J. Algebra 123 (1989), 457–77. 465Google Scholar
Neumann, M. M. and Velasco, M. V., Continuity of epimorphisms and derivations on vector-valued group algebras. Arch. Math. (Basel) 68 (1997), 151–8. 596Google Scholar
Miziolek, J. K., Müldner, T., and Rek, A., On topologically nilpotent algebras. Studia Math . 43 (1972), 4150. xxvi, 650, 651Google Scholar
Mocanu, Gh., Sur certains types de commutativité dans les algèbres de Banach. An. Univ. Bucuresti Mat. 37 (1988), 3641. 436Google Scholar
Mohammadzadeh, S. and Vishki, H. R. E., Arens regularity of module actions and the second adjoint of a derivation. Bull. Aust. Math. Soc . 77 (2008), 465–76. 268Google Scholar
Molnár, L., Modular bases in a Hilbert A-module. Czechoslovak Math. J . 42 (117) (1992), 649–56. 557Google Scholar
Molnár, L., A few conditions for a C -algebra to be commutative. Abstr. Appl. Anal. 2014, Art. ID 705836, 4 pp. 401Google Scholar
Moreno, A., Extending the norm from special Jordan triple systems to their associative envelopes. In Banach algebras’97 (Blaubeuren), pp. 363–75, de Gruyter, Berlin, 1998. xxiii, 475, 476Google Scholar
Moreno, A., The triple-norm extension problem: the nondegenerate complete case. Studia Math . 136 (1999), 91–7. xxiii, 475, 476Google Scholar
Moreno, A., Some recent results about the norm extension problem. In [705], pp. 125–31. xxiii, 462, 474, 475Google Scholar
Moreno, A. and Rodríguez, A., The norm extension problem: positive results and limits. II Congress on Examples and Counterexamples in Banach Spaces (Badajoz, 1996). Extracta Math . 12 (1997), 165–71. 462, 473, 474Google Scholar
Moreno, A. and Rodríguez, A., Algebra norms on tensor products of algebras, and the norm extension problem. Linear Algebra Appl . 269 (1998), 257305. xxiii, 472, 473, 474, 475Google Scholar
Müller, V., Nil, nilpotent and PI-algebras. In [1189], pp. 259–65. xxvi, 651Google Scholar
Neufang, M., On Mazur’s property and property (X). J. Operator Theory 60 (2008), 301–16. 238, 239Google Scholar
Ogasawara, T., A theorem on operator algebras. J. Sci. Hiroshima Univ. Ser. A . 18 (1955), 307–9. 400Google Scholar
Osborn, J. M. and Racine, M. L., Jordan rings with nonzero socle. Trans. Amer. Math. Soc . 251 (1979), 375–87. 598Google Scholar
Oudadess, M., Commutativité de certaines algèbres de Banach. Bol. Soc. Mat. Mexicana 28 (1983), 914. 436Google Scholar
Pedersen, G. K. and Størmer, E., Traces on Jordan algebras. Canad. J. Math . 34 (1982), 370–3. 339Google Scholar
Pełczyński, A., Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Acad. Polon. Sci . 10 (1962), 641–8. 266Google Scholar
Peralta, A. M., Little Grothendieck’s theorem for real JB -triples. Math. Z . 237 (2001), 531–45. 337, 346Google Scholar
Peralta, A. M., New advances on the Grothendieck’s inequality problem for bilinear forms on JB -triples. Math. Inequal. Appl . 8 (2005), 721. 346Google Scholar
Peralta, A. M., Some remarks on weak compactness in the dual space of a JB -triple. Tôhoku Math. J . 58 (2006), 149–59. 335, 340Google Scholar
Peralta, A. M. and Rodríguez, A., Grothendieck’s inequalities for real and complex JBW -triples. Proc. London Math. Soc . 83 (2001), 605–25. xx, 268, 274, 338, 340, 341, 342, 344, 345, 346Google Scholar
Peralta, A. M. and Rodríguez, A., Grothendieck’s inequalities revisited. In [1141], pp. 409–23. 346Google Scholar
Pérez de Guzmán, I., Structure theorems for alternative H -algebras. Math. Proc. Cambridge Philos. Soc. 94 (1983), 437–46. xxv, 549Google Scholar
Pérez de Guzmán, I., Annihilator alternative algebras. Pacific J. Math. 107 (1983), 8994. 584Google Scholar
Pfitzner, H., L-summands in their biduals have Pełczyński’s property (V). Studia Math. 104 (1993), 91–8. xix, 245, 267Google Scholar
Pfitzner, H., Separable L-embedded Banach spaces are unique preduals. Bull. Lond. Math. Soc. 39 (2007), 1039–44. 241Google Scholar
Pfitzner, H., Phillips’ lemma for L-embedded Banach spaces. Arch. Math. (Basel) 94 (2010), 547–53. 267Google Scholar
Pfitzner, H., A well-known criterion of Pełczyński’s Property (V). Private communication, September 2014. xix, 2, 245, 266, 267Google Scholar
Pfitzner, H., Predual uniqueness coming from the generalized property (X) à la Godefroy–Talagrand. Private communication, April 2017. 238, 241Google Scholar
Phillips, R. S., On symplectic mappings of contraction operators. Studia Math. 31 (1968) 1527. 207Google Scholar
Pinter-Lucke, J., Commutativity conditions for rings: 1950–2005. Expo. Math. 25 (2007), 165–74. 401Google Scholar
Pisier, G., Grothendieck’s theorem for noncommutative C -algebras, with an appendix on Grothendieck’s constants. J. Funct. Anal. 29 (1978), 397415. 342, 343Google Scholar
Pisier, G., Grothendieck’s theorem, past and present. Bull. Amer. Math. Soc. 49 (2012), 237323. xx, 342, 343Google Scholar
Poliquin, R. A. and Zizler, V. E., Optimization of convex functions on w -compact sets. Manuscripta Math. 68 (1990), 249270. 338Google Scholar
Pritchard, F. L., Ideals in the multiplication algebra of a nonassociative K-algebra. Comm. Algebra 21 (1993), 4541–59. 546Google Scholar
Pyatetskii-Shapiro, I. I., On a problem proposed by E. Cartan. Dokl. Akad. Nauk SSSR 124 (1959), 272–3. 210Google Scholar
Pym, J. S., The convolution of functionals on spaces of bounded functions. Proc. London Math. Soc. 15 (1965), 84104. 267Google Scholar
Randrianantoanina, N., Pełczyński’s property (V) for symmetric operator spaces. Proc. Amer. Math. Soc. 125 (1997), 801–6. 267Google Scholar
Robbin, J. W., On the existence theorem for differential equations. Proc. Amer. Math. Soc. 19 (1968), 1005–6. 137Google Scholar
Rodríguez, A., La continuidad del producto de Jordan implica la del ordinario en el caso completo semiprimo. In: Contribuciones en probabilidad, estadística matemática, enseñanza de la matemática y análisis, pp. 280–8, Secretariado de Publicaciones de la Universidad de Granada, Granada, 1979. xxiii, 474Google Scholar
Rodríguez, A., A note on Arens regularity. Quart. J. Math. Oxford 38 (1987), 91–3. 267, 268Google Scholar
Rodríguez, A., On the strong topology of a JBW -triple. Quart. J. Math. Oxford 42 (1991), 99103. xx, 274, 335, 337, 338, 339Google Scholar
Rodríguez, A., Non-associative normed algebras: geometric aspects. In [1189], pp. 299–311. 421, 462Google Scholar
Rodríguez, A., Estructuras de Jordan en Análisis. Rev. Real Acad. Cienc. Exact. Fís. Natur. Madrid 88 (1994), 309–17. 462Google Scholar
Rodríguez, A. and Velasco, M. V., Continuity of homomorphisms and derivations on normed algebras which are tensor products of algebras with involution. Rocky Mountain J. Math. 32 (2002), 1045–55. xxiii, 474, 475Google Scholar
Rodríguez, A. and Villena, A. R., Centroid and extended centroid of JB -algebras, In [734], pp. 223–32. 408Google Scholar
Rosentahl, P. and Soltysiak, A., Formulas for the joint spectral radius of non-commuting Banach algebra elements. Proc. Amer. Math. Soc. 123 (9) (1995), 2705–8. 651Google Scholar
Ruckle, W. H., The infinite sum of closed subspaces of an F-space. Duke Math. J. 31 (1964), 543–54. 584Google Scholar
Runde, V., Review of [462]. MR1706325 (2000f:46067). 596Google Scholar
Russo, B., Derivations and projections on Jordan triples: an introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis. In Advanced courses of mathematical analysis V, pp. 118227, World Sci. Publ., Hackensack, NJ, 2016. 346Google Scholar
Sakai, S., A characterization of W -algebras. Pacific J. Math. 6 (1956), 763–73. 19Google Scholar
Sakai, S., Weakly compact operators on operator algebras. Pacific J. Math. 14 (1964), 659–64. 274, 336Google Scholar
Sakai, S., On topologies of finite W -algebras. Illinois J. Math. 9 (1965), 236–41. 334Google Scholar
Saworotnow, P. P., A generalized Hilbert space. Duke Math. J. 35 (1968), 191–7. 556Google Scholar
Saworotnow, P. P., Trace-class and centralizers of an H -algebra. Proc. Amer. Math. Soc. 26 (1970), 101–4. 550Google Scholar
Saworotnow, P. P. and Friedell, J. C., Trace-class for an arbitrary H -algebra. Proc. Amer. Math. Soc. 26 (1970), 95100. 550Google Scholar
Schafer, R. D., On structurable algebras. J. Algebra 92 (1985), 400–12. 555Google Scholar
Schafer, R. D., Invariant forms on central simple structurable algebras. J. Algebra 122 (1989), 112–7. 556Google Scholar
Schatten, R., The cross-space of linear transformations. Ann. of Math. 47 (1946), 7384. 550Google Scholar
Schatten, R. and von Neumann, J., The cross-space of linear transformations. II. Ann. of Math. 47 (1946), 608–30. 550Google Scholar
Schatten, R. and von Neumann, J., The cross-space of linear transformations. III. Ann. of Math. 49 (1948), 557–82. 550Google Scholar
Sherman, S., Order in operator algebras. Amer. J. Math. 73 (1951), 227–32. 400Google Scholar
Shestakov, I. P., Speciality and deformations of algebras. In: Algebra: Proceedings of the International Algebraic Conference on the Occasion of the 90th Birthday of A. G. Kurosh (Moscow, 1998), pp. 345–56, de Gruyter, Berlin, 2000. xxii, 470Google Scholar
Shulman, V. S., On invariant subspaces of Volterra operators. (Russian) Funk. Anal. i Prilozen 18 (1984), 84–5. xxvi, 651Google Scholar
Shulman, V. S., Invariant subspaces and spectral mapping theorems. In [1189], pp. 313–25. 651Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals. I. Basic properties, tensor products and joint quasinilpotence. In Topological algebras, their applications, and related topics (Ed. by Jarosz, K. and Soltysiak, A.), pp. 293333, Banach Center Publ. 67, Polish Acad. Sci., Warsaw, 2005. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals, II. Applications to spectral theory of multiplication operators. In Elementary operators and their applications (Belfast, 2009) (Ed. by Curto, R. E. and Mathieu, M.), pp. 45114, Oper. Theory Adv. Appl., 212, Birkhäuser/Springer Basel AG, Basel, 2011. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals and the joint spectral radius. (Russian) Funktsional. Anal. i Prilozhen. 46 (2012), 6182; translation in Funct. Anal. Appl. 46 (2012), 287–304. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals, V. From algebra to spectral theory. In Algebraic methods in functional analysis. The Victor Shulman anniversary volume (Ed. by Todorov, I. G. and Turowska, L.), pp. 171280, Oper. Theory Adv. Appl., 233, Birkhäuser/Springer Basel AG, Basel, 2013. 652Google Scholar
Simons, S., On the Dunford–Pettis property and Banach spaces that contain c 0 . Math. Ann. 216 (1975), 225–31. 266Google Scholar
Sinclair, A. M., Homomorphisms from C -algebras. Proc. London Math. Soc. 29 (1974), 435–52. Corrigendum: Proc. London Math. Soc. 32 (1976), 322. 548Google Scholar
Sinclair, A. M. and Tullo, A. W., Noetherian Banach algebras are finite dimensional. Math. Ann. 211 (1974), 151–3. 601Google Scholar
Smirnov, O. N., Simple and semisimple structurable algebras. (Russian) Algebra i Logika 29 (1990), 571–96; translation in Algebra and Logic 29 (1990), 377–94. 555Google Scholar
Smith, J. F., The structure of Hilbert modules. J. London Math. Soc. 8 (1974), 741–9. 556Google Scholar
Smith, R. R. and Ward, J. D., M-ideal structure in Banach algebras. J. Funct. Anal. 27 (1978), 337–49. 19Google Scholar
Soltysiak, A., On the joint spectral radii of commuting Banach algebra elements. Studia Math. 105 (1993), 93–9. 651Google Scholar
Stacey, P. J., Type I 2 JBW-algebras. Quart. J. Math. Oxford 33 (1982), 115–27. 416Google Scholar
Stachó, L. L., A short proof of the fact that biholomorphic automorphisms of the unit ball in certain L p spaces are linear. Acta Sci. Math. (Szeged) 41 (1979), 381–3. 207Google Scholar
Stachó, L. L., On nonlinear projections of vector fields. In Convex analysis and chaos (Sakado, 1998), pp. 4754, Josai Math. Monogr. 1, Josai Univ., Sakado, 1999. 207Google Scholar
Stampfli, J. G., The norm of a derivation. Pacific J. Math. 33 (1970), 737–47. 550Google Scholar
Steptoe, A. C. P., JC -triples and inner ideals in universally reversible JC -algebras. Quart. J. Math. 56 (2005), 397402. 460Google Scholar
Stern, J., Some applications of model theory in Banach space theory. Ann. Math. Logic 9 (1976), 49121. 236Google Scholar
Stone, M. H., Boundedness properties in function-lattices. Canadian J. Math. 1 (1949), 176–86. 421 Google Scholar
Takesaki, M., On the conjugate space of operator algebra. Tôhoku Math. J. 10 (1958), 194203. 334Google Scholar
Taylor, D. C., The strict topology for double centralizer algebras. Trans. Amer. Math. Soc. 150 (1970) 633–43. 400Google Scholar
Tullo, A. W., Conditions on Banach algebras which imply finite dimensionality. Proc. Edinburgh Math. Soc. 20 (1976), 15. 598Google Scholar
Turovskii, Yu. V., Spectral properties of elements of normed algebras, and invariant subspaces. (Russian) Funktsional. Anal. i Prilozhen. 18 (1984), 77–8; translation in Funct. Anal. Appl. 18 (1984), 152–4. 651Google Scholar
Turovskii, Yu. V. and Shulman, V. S., Radicals in Banach algebras, and some problems in the theory of radical Banach algebras. (Russian) Funktsional. Anal. i Prilozhen. 34 (2001), no. 4, 8891; translation in Funct. Anal. Appl. 35 (2001), 312–4. 652Google Scholar
Turovskii, Yu. V. and Shulman, V. S., Topological radicals and the joint spectral radius. (Russian) Funktsional. Anal. i Prilozhen. 46 (2012), 6182; translation in Funct. Anal. Appl. 46 (2012), 287–304. 652Google Scholar
Ülger, A., Weakly compact bilinear forms and Arens regularity. Proc. Amer. Math. Soc. 101 (1987), 697704. 268Google Scholar
Umegaki, H., Weak compactness in an operator space. Kōdai Math. Sem. Rep. 8 (1956), 145–51. 334Google Scholar
Unsain, I., Classification of the simple separable real L -algebras. J. Differential Geometry 7 (1972), 423–51. 554Google Scholar
Upmeier, H., Über die Automorphismengruppen von Banach-Mannigfaltigkeiten mit invarianter Metrik. Math. Ann. 223 (1976), 279–88. 174Google Scholar
Upmeier, H., Remarks on the Campbell–Hausdorff formula for holomorphic vector fields. Private communication, June 2017. xix, 174Google Scholar
Vigué, J.-P., Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. Ann. Sci. École Norm. Sup. (4) 9 (1976), 203–81. xix, 87, 159, 174, 211Google Scholar
Vigué, J.-P., Les domaines bornés symétriques d’un espace de Banach complexe et les systémes triples de Jordan. Math. Ann. 229 (1977), 223–31. 211Google Scholar
Vigué, J.-P., Sur la décomposition d’un domaine borné symétrique en produit continu de domaines bornés symétriques irréductibles. Ann. Sci. École Norm. Sup. (4) 14 (1981), 453–63. 241Google Scholar
Villena, A. R., Continuity of derivations on a complete normed alternative algebra. J. Inst. Math. Comput. Sci. Math. Ser. 3 (1990), 99106. 548Google Scholar
Viola Devapakkiam, C., Hilbert space methods in the theory of Jordan algebras. I. Math. Proc. Cambridge Philos. Soc. 78 (1975), 293300. xxv, 552Google Scholar
Viola Devapakkiam, C. and Rema, P. S., Hilbert space methods in the theory of Jordan algebras. II. Math. Proc. Cambridge Philos. Soc. 79 (1976), 307–19. xxv, 552Google Scholar
Weaver, N., A prime C -algebra that is not primitive. J. Funct. Anal. 203 (2003), 356–61. 467Google Scholar
Wilkins, T. J. D., Spectrum-finite ideals of Jordan-Banach algebras. J. London Math. Soc. 54 (1996), 359–68. 601Google Scholar
Yeadon, F. J., A note on the Mackey topology of a von Neumann algebra. J. Math. Anal. Appl. 45 (1974), 721–2. 336Google Scholar
Yood, B., Closed prime ideals in topological rings. Proc. London Math. Soc. 24 (1972), 307–23. 583, 584Google Scholar
Youngson, M. A., Review of [710]. Bull. Lond. Math. Soc. 44 (2012), 1304–7. xixGoogle Scholar
Zalar, B., Continuity of derivations on Mal’cev H -algebras. Math. Proc. Cambridge Philos. Soc. 110 (1991), 455–9. 548Google Scholar
Zalar, B., On derivations of H -algebras. University of Ljubljana, Preprint Series of the Department of Mathematics, Vol. 29 (1991), 356. 548Google Scholar
Zalar, B., A note on the definition of a nonassociative H -triple. University of Ljubljana, Preprint Series of the Department of Mathematics, Vol. 30 (1992), 361. 561Google Scholar
Zalar, B., Continuity of derivation pairs on alternative and Jordan H -triples. Boll. Un. Mat. Ital. B 7 (1993), 215–30. 559Google Scholar
Zalar, B., Theory of Hilbert triple systems. Yokohama Math. J. 41 (1994), 95126. 558Google Scholar
Zel’manov, E. I., Jordan algebras with finiteness conditions. Algebra Logic 17 (1978), 450–7. 562Google Scholar
Zel’manov, E. I., On prime Jordan algebras. Algebra Logic 18 (1979), 162–75. 364, 437Google Scholar
Zel’manov, E. I., Lie algebras with algebraic associated representation. (Russian) Mat. Sb. (N.S.) 121 ( 163 ) (1983), 545–61; translation in Math. USSR-Sb. 49 (1984), 537–52. 658Google Scholar
Zel’manov, E. I., Primary Jordan triple systems. Sibirsk. Mat. Zh. 24 (1983), 2337. xxii, 437, 438, 459Google Scholar
Zel’manov, E. I., Primary Jordan triple systems. II. Sibirsk. Mat. Zh. 25 (1984), 5061. xxii, 437, 438, 447, 459Google Scholar
Zel’manov, E. I., Lie algebras with a finite grading. Math. USSR Sb. 52 (1985), 347–85. 600Google Scholar
Zel’manov, E. I., On Engel Lie algebras. Soviet Math. Dokl. 35 (1987), 44–7. 658Google Scholar
Zizler, V., On some extremal problems in Banach spaces. Math. Scand. 32 (1973), 214–24. xx, 274, 337Google Scholar
Abraham, R., Marsden, J. E., and Ratiu, T., Manifolds, tensor analysis, and applications. Second edition. Applied Mathematical Sciences, 75. Springer-Verlag, New York, 1988. 135 Google Scholar
Alvermann, K., Normierte nichtkommutative Jordan-Algebren vom Typ I. PhD thesis, Braunschweig 1982. 421 Google Scholar
Behrends, E., M-structure and the Banach–Stone theorem. Lecture Notes in Math. 736, Springer, Berlin, 1979. 350, 351, 398Google Scholar
Bierstedt, K. D., Bonet, J., Maestre, M., and Schmets, J. (eds.), Recent progress in functional analysis. Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, Valencia, Spain, July 3–7, 2000. North Holland Math. Studies 189, Elsevier, Amsterdam 2001. 679, 708Google Scholar
Bonfiglioli, A. and Fulci, R., Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin. Lecture Notes in Math. 2034, Springer, Heidelberg, 2012. 154, 155, 174Google Scholar
Bourbaki, N., Éléments de mathématique: groupes et algèbres de Lie. Chapitres 2 et 3. Springer-Verlag, Berlin, 2006. 154, 155, 174Google Scholar
Cabrera, M., H-álgebras no asociativas reales. H-álgebras de Malcev complejas y reales . PhD thesis, Granada 1987. Tesis Doctorales de la Universidad de Granada, Secretariado de Publicaciones de la Universidad de Granada, 1988. 552, 555Google Scholar
Cartan, H., Sur les groupes de transformations analytiques. Act. Sci. Ind. 198, Hermann, Paris, 1935. 87 Google Scholar
Cartan, H., Cours de calcul différentiel. Second edition. Hermann, Paris, 1977. 53 Google Scholar
Chaperon, M., Calcul différentiel et calcul intégral. Second edition. Dunod, Paris, 2008. 53 Google Scholar
Coleman, R., Calculus on normed vector spaces. Universitext. Springer, New York, 2012. 53, 135, 136Google Scholar
Conway, J. B., Functions of one complex variable. Second edition. Grad. Texts in Math. 11. Springer-Verlag, New York-Berlin, 1978. 44, 55, 58, 101, 185Google Scholar
Dales, H. G., Dashiell, F. K., Jr., Lau, A. T.-M., and Strauss, D., Banach Spaces of Continuous Functions as Dual Spaces. CMS Books Math., Springer, New York, 2016. 421 Google Scholar
Diestel, J., Sequences and series in Banach spaces. Grad. Texts in Math. 92. Springer-Verlag, New York, 1984. 239, 245, 253, 258, 266, 267, 279Google Scholar
Dieudonné, J., Éléments d’analyse. Tome I. Fondements de l’analyse moderne . Third edition. Translated from the English by D. Huet. With a foreword by Gaston Julia. Cahiers Scientifiques XXVIII. Gauthier-Villars, Paris, 1981. 53, 135, 136Google Scholar
Dieudonné, J., Éléments d’analyse . Tome II: Chapitres XII à XV. Cahiers Scientifiques XXXI Gauthier-Villars, Paris, 1968. 335 Google Scholar
Dineen, S., Complex analysis in locally convex spaces. North-Holland Math. Stud. 57. North-Holland Publishing Co., Amsterdam, 1981. 53 Google Scholar
Dineen, S., Complex analysis on infinite-dimensional spaces. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 1999. xxvi, 53Google Scholar
Doran, R. S. and Wichmann, J., Approximate identities and factorization in Banach modules . Lecture Notes in Math. 768, Springer, Berlin, 1979. xxvi, 651, 652Google Scholar
Fernández, A., Teoremas de Wedderburn-Zorn en álgebras alternativas normadas completas, PhD thesis, Universidad de Granada 1983. 583, 584Google Scholar
Fernández, A., Jordan techniques in Lie algebras. Book in progress. 600Google Scholar
Franzoni, T. and Vesentini, E., Holomorphic maps and invariant distances . North-Holland Math. Stud. 69, North-Holland Publishing Co., Amsterdam, 1980. 53, 87Google Scholar
Hervé, M., Analyticity in infinite-dimensional spaces. de Gruyter Studies in Mathematics, 10. Walter de Gruyter & Co., Berlin, 1989. 53 Google Scholar
Horváth, J., Topological vector spaces and distributions. Volume I. Addison-Wesley Publishing Co., Reading, Massachusetts-London-Don Mills, Ontario, 1966. 7, 290Google Scholar
Istrǎtescu, V. I., Inner product structures. Theory and applications. Mathematics and its Applications, 25. D. Reidel Publishing Co., Dordrecht, 1987. 551, 557Google Scholar
Jarchow, H., Locally convex spaces. Mathematische Leitfäden. B. G. Teubner, Stuttgart, 1981. 335 Google Scholar
Johnstone, P. T., Stone spaces. Reprint of the 1982 edition. Cambridge Studies in Advanced Mathematics, 3. Cambridge University Press, Cambridge, 1986. 421 Google Scholar
Jungers, R., The joint spectral radius. Theory and applications. Lecture Notes in Control and Information Sciences, 385. Springer-Verlag, Berlin, 2009. 651 Google Scholar
Kadets, V., Martín, M., Merí, J., and Pérez, A., Spear operators between Banach spaces . Lecture Notes in Math., Springer. 209 Google Scholar
Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vol. II. Advanced theory . Grad. Stud. Math. 16, American Mathematical Society, Providence, RI, 1997. 19 Google Scholar
Kelley, J. L. and Namioka, I., Linear topological spaces. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, NJ, 1963. 288 Google Scholar
Koecher, M., An elementary approach to bounded symmetric domains, Lecture Notes (Rice University, Houston, TX, 1969). 211 Google Scholar
Lang, S., Differential and Riemannian manifolds . Third edition. Grad. Texts in Math. 160. Springer-Verlag, New York, 1995. 135 Google Scholar
Lee, J. M., Introduction to smooth manifolds . Second Edition. Grad. Texts in Math. 218. Springer, New York, 2013. 135 Google Scholar
Lelong-Ferrand, J. and Arnaudiès, J. M., Cours de mathématiques. Tome 2: Analyse . Fourth edition. Dunod, Paris, 1977. 53 Google Scholar
Mellon, P., An introduction to bounded symmetric domains . Textos de Matemática. Série B. Universidade de Coimbra, Departamento de Matemática, Coimbra, 2000. 210, 211Google Scholar
Moreno, A., Álgebras de Jordan-Banach primitivas, PhD thesis, Universidad de Granada 1995. 470 Google Scholar
Mujica, J., Complex analysis in Banach spaces . Dover Publications, Inc. Mineola, New York, 2010. 53, 87Google Scholar
Narasimhan, R., Several complex variables . Chicago Lectures in Mathematics. The University of Chicago Press, Chicago and London, 1971. 87, 207Google Scholar
Neher, E., Jordan triple systems by the grid approach. Lecture Notes in Math. 1280, Springer-Verlag, Berlin, 1987. 557 Google Scholar
Pedersen, G. K., C-algebras and their automorphism groups. London Math. Soc. Monogr. 14, Academic Press, London-New York, 1979. 408 Google Scholar
Pérez de Guzmán, I., Álgebras alternativas normadas. Teorema de estructura para H-álgebras alternativas . PhD thesis, Granada 1977. Tesis Doctorales de la Universidad de Granada 266, Secretariado de Publicaciones de la Universidad de Granada, 1980. 549 Google Scholar
Reich, S. and Shoikhet, D., Nonlinear semigroups, fixed points, and geometry of domains in Banach spaces. Imperial College Press, London, 2005. 79, 87, 88, 135Google Scholar
Reutenauer, C., Free Lie algebras. London Mathematical Society Monographs. New Series, 7. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993. 154, 174Google Scholar
Ringrose, J. R., Compact non-self-adjoint operators. Van Nostrand Reinhold Co., London, 1971. 481, 524Google Scholar
Saitô, K. and Wright, J. D. M., Monotone complete C-algebras and generic dynamics. Springer Monographs in Mathematics. Springer, London, 2015. 19 Google Scholar
Singer, I., Bases in Banach spaces . I. Die Grundlehren der mathematischen Wissenschaften, Band 154. Springer-Verlag, New York-Berlin, 1970. 239 Google Scholar
Takesaki, M., Theory of operator algebras. I. Reprint of the first (1979) edition. Encyclopaedia of Mathematical Sciences, 124. Operator Algebras and Noncommutative Geometry, 5. Springer-Verlag, Berlin, 2002. 332, 334, 335Google Scholar
Upmeier, H., Über die Automorphismengruppen beschränkter Gebiete in Banachräumen. PhD thesis, Tübingen 1975. 174 Google Scholar
Vigué, J.-P., Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. PhD thesis, Publication Mathématique d’Orsay, 1976. 87, 135, 174, 211Google Scholar
Willard, S., General topology. Reprint of the 1970 original [Addison-Wesley, Reading, MA; MR0264581]. Dover Publications, Inc., Mineola, NY, 2004. 87, 280Google Scholar
Zemánek, J. (Editor), Functional analysis and operator theory (Warsaw, 1992). Banach Center Publ., 30, Polish Acad. Sci., Warsaw, 1994. 665, 707, 709Google Scholar
Acosta, M. D., Becerra, J., and Rodríguez, A., Weakly open sets in the unit ball of the projective tensor product of Banach spaces. J. Math. Anal. Appl. 383 (2011), 461–73.Google Scholar
Adams, J. F., On the structure and applications of the Steenrod algebra. Comment. Math. Helv. 32 (1958), 180214.CrossRefGoogle Scholar
Akemann, C. A. and Pedersen, G. K., Complications of semicontinuity in C -algebra theory. Duke Math. J. 40 (1973), 785–95. 346Google Scholar
Akemann, C. A. and Pedersen, G. K., Facial structure in operator algebra theory. Proc. London Math. Soc. 64 (1992), 418–48.Google Scholar
Akemann, C. A. and Weaver, N., Geometric characterizations of some classes of operators in C -algebras and von Neumann algebras. Proc. Amer. Math. Soc. 130 (2002), 3033–7.Google Scholar
Albert, A. A., On a certain algebra of quantum mechanics. Ann. of Math. 35 (1934), 6573. Reprinted in [692], pp. 85–93.CrossRefGoogle Scholar
Albert, A. A., Quadratic forms permitting composition. Ann. of Math. 43 (1942), 161–77. Reprinted in [692], pp. 219–35.Google Scholar
Albert, A. A., The radical of a non-associative algebra. Bull. Amer. Math. Soc. 48 (1942), 891–7. Reprinted in [692], pp. 277–83. 546Google Scholar
Albert, A. A., Absolute valued real algebras. Ann. of Math. 48 (1947), 495501. Reprinted in [691], pp. 643–9.Google Scholar
Albert, A. A., A structure theory for Jordan algebras. Ann. of Math. 48 (1947), 546–67. Reprinted in [692], pp. 401–22.Google Scholar
Albert, A. A., On the power-associativity of rings. Summa Brasil. Math. 2 (1948), 2132. Reprinted in [692], pp. 423–35.Google Scholar
Albert, A. A., Power-associative rings. Trans. Amer. Math. Soc. 608 (1948), 552–93. Reprinted in [692], pp. 437–78. 273Google Scholar
Albert, A. A., Absolute valued algebraic algebras. Bull. Amer. Math. Soc. 55 (1949), 763–8. Reprinted in [691], pp. 651–6.Google Scholar
Albert, A. A., A note of correction. Bull. Amer. Math. Soc. 55 (1949), 1191.Google Scholar
Alfsen, E. M., Shultz, F. W., and Størmer, E., Gelfand, ANeumark theorem for Jordan algebras. Adv. Math. 28 (1978), 1156. 398, 401Google Scholar
Allan, G. R., Some simple proofs in holomorphic spectral theory. In Perspectives in operator theory, pp. 915, Banach Center Publ. 75, Polish Acad. Sci. Inst. Math., Warsaw, 2007.Google Scholar
Alvermann, K., The multiplicative triangle inequality in noncommutative JB- and JB -algebras. Abh. Math. Sem. Univ. Hamburg 55 (1985), 91–6.Google Scholar
Alvermann, K., Real normed Jordan Banach algebras with an involution. Arch. Math. (Basel) 47 (1986), 135–50.CrossRefGoogle Scholar
Alvermann, K. and Janssen, G., Real and complex non-commutative Jordan Banach algebras. Math. Z. 185 (1984), 105–13. xix, xx, 19, 267, 268, 334, 335, 398, 411, 421Google Scholar
Ambrose, W., Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364886. xxiii, xxv, 477, 545, 550Google Scholar
Anquela, J. A., Montaner, F., and Cortés, T., On primitive Jordan algebras. J. Algebra 163 (1994), 663–74. xxii, 462, 466CrossRefGoogle Scholar
Aparicio, C., Ocaña, F. G., Payá, R., and Rodríguez, A., A non-smooth extension of Fréchet differentiability of the norm with applications to numerical ranges. Glasgow Math. J. 28 (1986), 121–37.Google Scholar
Aparicio, C. and Rodríguez, A., Sobre el espectro de derivaciones y automorfismos de las álgebras de Banach. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 79 (1985), 113–18.Google Scholar
Araki, H. and Elliott, G. A., On the definition of C -algebras. Publ. Res. Inst. Math. Sci. 9 (1973/74), 93112.Google Scholar
Arazy, J., Isometries of Banach algebras satisfying the von Neumann inequality. Math. Scand. 74 (1994), 137–51. 136, 207Google Scholar
Arazy, J. and Solel, B., Isometries of nonselfadjoint operator algebras. J. Funct. Anal. 90 (1990), 284305. 207CrossRefGoogle Scholar
Arendt, W., Chernoff, P. R., and Kato, T., A generalization of dissipativity and positive semigroups. J. Operator Theory 8 (1982), 167–80.Google Scholar
Arens, R., Operations induced in function classes. Monatsh. Math. 55 (1951), 119.CrossRefGoogle Scholar
Arens, R., The adjoint of a bilinear operation. Proc. Amer. Math. Soc. 2 (1951), 839–48.Google Scholar
Arens, R. and Kaplansky, I., Topological representation of algebras. Trans. Amer. Math. Soc. 63 (1948), 457–81.Google Scholar
Argyros, S. A. and Felouzis, V., Interpolating hereditarily indecomposable Banach spaces. J. Amer. Math. Soc. 13 (2000), 243–94.CrossRefGoogle Scholar
Argyros, S. A. and Haydon, R. G., A hereditarily indecomposable L -space that solves the scalar-plus-compact problem. Acta Math. 206 (2011), 154.Google Scholar
Argyros, S. A., López-Abad, J., and Todorcevic, S., A class of Banach spaces with few non-strictly singular operators. J. Funct. Anal. 222 (2005), 306–84.Google Scholar
Aron, R. M. and Lohman, R. H., A geometric function determined by extreme points of the unit ball of a normed space. Pacific J. Math. 127 (1987), 209–31.Google Scholar
Arosio, A., Locally convex inductive limits of normed algebras. Rend. Sem. Mat. Univ. Padova 51 (1974), 333–59.Google Scholar
Auerbach, H., Sur les groupes linéaires I, II, III. Studia Math . 4 (1934), 113–27; Ibid. 4 (1934), 158–66; Ibid. 5 (1935), 43–9.Google Scholar
Aupetit, B., Symmetric almost commutative Banach algebras. Notices Amer. Math. Soc. 18 (1971), 559–60.Google Scholar
Aupetit, B., Caractérisation spectrale des algèbres de Banach commutatives. Pacific J. Math. 63 (1976), 2335.CrossRefGoogle Scholar
Aupetit, B., Caractérisation spectrale des algèbres de Banach de dimension finie. J. Funct. Anal. 26 (1977), 232–50.Google Scholar
Aupetit, B., The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras. J. Funct. Anal. 47 (1982), 16. x, 597Google Scholar
Aupetit, B., Recent trends in the field of Jordan–Banach algebras. In [1189], pp. 9–19. 597Google Scholar
Aupetit, B., Analytic Multifunctions and their applications. In Complex potential theory (ed. Gauthier, P. M.), pp. 174, Kluwer Academic Publishers, Dordrecht– Boston–London 1994.Google Scholar
Aupetit, B., Spectral characterization of the socle in Jordan–Banach algebras. Math. Proc. Cambridge Philos. Soc. 117 (1995), 479–89. 601CrossRefGoogle Scholar
Aupetit, B., Trace and spectrum preserving linear mappings in Jordan–Banach algebras. Monatsh. Math. 125 (1998), 179–87. 601Google Scholar
Aupetit, B. and Baribeau, L., Sur le socle dans les algèbres de Jordan–Banach. Canad. J. Math. 41 (1989), 1090–100. 599Google Scholar
Aupetit, B. and Maouche, A., Trace and determinant in Jordan–Banach algebras. Publ. Mat. 46 (2002), 316. 601Google Scholar
Aupetit, B. and Mathieu, M., The continuity of Lie homomorphisms. Studia Math. 138 (2000), 193–99. 603Google Scholar
Aupetit, B. and Youngson, M. A., On symmetry of Banach Jordan algebras. Proc. Amer. Math. Soc. 91 (1984), 364–6. 597Google Scholar
Avilés, A. and Koszmider, P., A Banach space in which every injective operator is surjective. Bull. London Math. Soc. 45 (2013), 1065–74.Google Scholar
Baer, R., Radical ideals. Amer. J. Math. 65 (1943), 537–68.Google Scholar
Baez, J. C., The octonions. Bull. Amer. Math. Soc. 39 (2002), 145205. Errata. Ibid. 42 (2005), 213.Google Scholar
Baillet, M., Analyse spectrale des opérateurs hermitiens d’une espace de Banach. J. London Math. Soc. 19 (1979), 497508.Google Scholar
Balachandran, V. K., Simple L -algebras of classical type. Math. Ann. 180 (1969), 205–19. 554Google Scholar
Balachandran, V. K. and Rema, P. S., Uniqueness of the norm topology in certain Banach Jordan algebras. Publ. Ramanujan Inst. 1 (1969), 283–9. 597Google Scholar
Balachandran, V. K. and Swaminatan, N., Real H -algebras. J. Funct. Anal. 65 (1986), 6475. 551CrossRefGoogle Scholar
Bandyopadhyay, P., Jarosz, K., and Rao, T. S. S. R. K., Unitaries in Banach spaces. Illinois J. Math. 48 (2004), 339–51.Google Scholar
Barnes, B. A., Locally B -equivalent algebras. Trans. Amer. Math. Soc. 167 (1972), 435–42.Google Scholar
Barnes, B. A., Locally B -equivalent algebras II. Trans. Amer. Math. Soc. 176 (1973), 297303.Google Scholar
Barnes, B. A., A note on invariance of spectrum for symmetric Banach ∗-algebras. Proc. Amer. Math. Soc. 126 (1998), 3545–7.Google Scholar
Barton, T. J. and Friedman, Y., Bounded derivations of JB -triples. Quart. J. Math. Oxford 41 (1990), 255–68. xx, 274, 337, 338Google Scholar
Bauer, F. L., On the field of values subordinate to a norm. Numer. Math. 4 (1962), 103–11.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Banach algebras with large groups of unitary elements. Quart. J. Math. Oxford 58 (2007), 203–20.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Banach spaces whose algebras of operators have a large group of unitary elements. Math. Proc. Camb. Phil. Soc. 144 (2008), 97108.Google Scholar
Becerra, J., Burgos, M., Kaidi, A., and Rodríguez, A., Nonassociative unitary Banach algebras. J. Algebra 320 (2008), 3383–97.Google Scholar
Becerra, J., Cowell, S., Rodríguez, A., and Wood, G. V., Unitary Banach algebras. Studia Math. 162 (2004), 2551.Google Scholar
Becerra, J., López, G., Peralta, A. M., and Rodríguez, A., Relatively weakly open sets in closed balls of Banach spaces, and real JB -triples of finite rank. Math. Ann. 330 (2004), 4558. 243, 274, 336Google Scholar
Becerra, J., López, G., and Rodríguez, A., Relatively weakly open sets in closed balls of C -algebras. J. London Math. Soc. 68 (2003), 753–61. 274, 336, 421Google Scholar
Becerra, J., Moreno, A., and Rodríguez, A., Absolute-valuable Banach spaces. Illinois J. Math. 49 (2005), 121–38.Google Scholar
Becerra, J. and Peralta, A. M., Subdifferentiability of the norm and the Banach–Stone theorem for real and complex JB -triples. Manuscripta Math. 114 (2004), 503–16.Google Scholar
Becerra, J. and Rodríguez, A., Isometric reflections on Banach spaces after a paper of A. Skorik and M. Zaidenberg. Rocky Mountain J. Math. 30 (2000), 6383.Google Scholar
Becerra, J. and Rodríguez, A., Transitivity of the norm on Banach spaces having a Jordan structure, Manuscripta Math. 102 (2000), 111–27. 210Google Scholar
Becerra, J. and Rodríguez, A., Characterizations of almost transitive superrreflexive Banach spaces. Comment. Math. Univ. Carolinae 42 (2001), 629–36.Google Scholar
Becerra, J. and Rodríguez, A., Transitivity of the norm on Banach spaces. Extracta Math. 17 (2002), 158.Google Scholar
Becerra, J. and Rodríguez, A., Strong subdifferentiability of the norm on JB -triples. Quart. J. Math. Oxford 54 (2003), 381–90.Google Scholar
Becerra, J. and Rodríguez, A., Big points in C -algebras and JB -triples. Quart. J. Math. Oxford 56 (2005), 141–64.Google Scholar
Becerra, J. and Rodríguez, A., Absolute-valued algebras with involution, and infinite-dimensional Terekhin’s trigonometric algebras. J. Algebra 293 (2005), 448–56.Google Scholar
Becerra, J. and Rodríguez, A., Non self-adjoint idempotents in C - and JB -algebras. Manuscripta Math. 124 (2007), 183–93.Google Scholar
Becerra, J. and Rodríguez, A., C - and JB -algebras generated by a non-self-adjoint idempotent. J. Funct. Anal. 248 (2007), 107–27.Google Scholar
Becerra, J. and Rodríguez, A., Locally uniformly rotund points in convex-transitive Banach spaces. J. Math. Anal. Appl. 360 (2009), 108–18.Google Scholar
Becerra, J., Rodríguez, A., and Wood, G. V., Banach spaces whose algebras of operators are unitary: a holomorphic approach. Bull. London Math. Soc. 35 (2003), 218–24. 210Google Scholar
Beddaa, A. and Oudadess, M., On a question of A. Wilansky in normed algebras. Studia Math. 95 (1989), 175–7.Google Scholar
Behncke, H., Hermitian Jordan Banach algebras. J. London Math. Soc. 20 (1979), 327–33. 597Google Scholar
Behncke, H. and Nyamwala, F. O., Two projections and one idempotent. Int. J. Pure Appl. Math. 52 (2009), 501–10.Google Scholar
Bell, J. P. and Small, L. W., A question of Kaplansky. J. Algebra 258 (2002), 386–8.Google Scholar
Bensebah, A., JV-algèbres et JH -algèbres. Canad. Math. Bull. 34 (1991), 447–55. 549, 597Google Scholar
Bensebah, A., Weakness of the topology of a JB -algebra. Canad. Math. Bull. 35 (1992), 449–54. 597Google Scholar
Benslimane, M. and Boudi, N., Alternative Noetherian Banach Algebras. Extracta Math. 12 (1997), 41–6. 601Google Scholar
Benslimane, M. and Boudi, N., Noetherian Jordan Banach algebras are finite-dimensional. J. Algebra 213 (1999), 340–50. 601Google Scholar
Benslimane, M., Fernández, A., and Kaidi, A., Caractérisation des algèbres de Jordan– Banach de capacité finie. Bull. Sci. Math. 112 (1988), 473–80. 597, 598, 599Google Scholar
Benslimane, M., Jaa, O., and Kaidi, A., The socle and the largest spectrum finite ideal. Quart. J. Math. Oxford 42 (1991), 17. 599, 601Google Scholar
Benslimane, M. and Kaidi, A., Structure des algèbres de Jordan–Banach non commutatives complexes régulières ou semi-simples à spectre fini. J. Algebra 113 (1988), 201–6. xxv, 596, 597, 598CrossRefGoogle Scholar
Benslimane, M. and Merrachi, N., Algèbres de Jordan Banach vérifiant ‖x‖‖x −1‖ = 1. J. Algebra 206 (1998), 129–34.Google Scholar
Benslimane, M. and Merrachi, N., Algèbres à puissances associatives normées sans J-diviseurs de zéro. Algebras Groups Geom. 16 (1999), 355–61.Google Scholar
Benslimane, M. and Moutassim, A., Some new class of absolute-valued algebras with left-unit. Adv. Appl. Clifford Algebras 21 (2011), 3140.Google Scholar
Benslimane, M. and Rodríguez, A., Caractérisation spectrale des algèbres de Jordan Banach non commutatives complexes modulaires annihilatrices. J. Algebra 140 (1991), 344–54. 599Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie derivations on Banach algebras. Proc. Edinburgh Math. Soc. 41 (1998), 625–30.Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie mappings of the skew elements of Banach algebras with involution. Proc. Amer. Math. Soc. 126 (1998), 2717–20.Google Scholar
Berenguer, M. I. and Villena, A. R., Continuity of Lie isomorphisms of Banach algebras. Bull. London Math. Soc. 31 (1999), 610.Google Scholar
Berenguer, M. I. and Villena, A. R., On the range of a Lie derivation on a Banach algebra. Comm. Algebra 28 (2000), 1045–50.Google Scholar
Berkson, E., Some characterizations of C -algebras. Illinois J. Math. 10 (1966), 18.Google Scholar
Beurling, A., Sur les intégrales de Fourier absolument convergentes et leur application à fonctionelle. In Neuvième congrès des mathématiciens scandinaves. Helsingfors, 1938, pp. 345–66.Google Scholar
Biss, D. K., Christensen, J. D., Dugger, D., and Isaksen, D. C., Large annihilators in Cayley–Dickson algebras II. Bol. Soc. Mat. Mexicana 13 (2007), 269–92.Google Scholar
Biss, D. K., Christensen, J. D., Dugger, D., and Isaksen, D. C., Eigentheory of Cayley– Dickson algebras. Forum Math. 21 (2009), 833–51.Google Scholar
Biss, D. K., Dugger, D., and Isaksen, D. C., Large annihilators in Cayley–Dickson algebras. Comm. Algebra 36 (2008), 632–64.Google Scholar
Blecher, D. and Magajna, B., Dual operator systems. Bull. London Math. Soc. 43 (2011), 311–20.Google Scholar
Blecher, D. P., Ruan, Z.-J., and Sinclair, A. M., A characterization of operator algebras. J. Funct. Anal. 89 (1990), 188201.Google Scholar
Boas, R. P., Entire functions of exponential type. Bull. Amer. Math. Soc. 48 (1942), 839–49.Google Scholar
Bohnenblust, H. F. and Karlin, S., Geometrical properties of the unit sphere of a Banach algebra. Ann. of Math. 62 (1955), 217–29.Google Scholar
Bollobás, B., An extension to the theorem of Bishop and Phelps. Bull. London Math. Soc. 2 (1970), 181–2.Google Scholar
Bollobás, B., The numerical range in Banach algebras and complex functions of exponential type. Bull. London Math. Soc. 3 (1971), 2733.Google Scholar
Bonsall, F. F., A minimal property of the norm in some Banach algebras. J. London Math. Soc. 29 (1954), 156–64.Google Scholar
Bonsall, F. F., Locally multiplicative wedges in Banach algebras. Proc. London Math. Soc. 30 (1975), 239–56.Google Scholar
Bonsall, F. F., Jordan algebras spanned by Hermitian elements of a Banach algebra. Math. Proc. Cambridge Philos. Soc. 81 (1977), no. 1, 313.Google Scholar
Bonsall, F. F., Jordan subalgebras of Banach algebras. Proc. Edinburgh Math. Soc. 21 (1978), 103–10.Google Scholar
Bonsall, F. F. and Crabb, M. J., The spectral radius of a Hermitian element of a Banach algebra. Bull. London Math. Soc. 2 (1970), 178–80.Google Scholar
Bonsall, F. F. and Duncan, J., Dually irreducible representations of Banach algebras, Quart. J. Math. Oxford 19 (1968), 97111.Google Scholar
Bott, R. and Milnor, J., On the parallelizability of the spheres. Bull. Amer. Math. Soc. 64 (1958), 87–9.Google Scholar
Böttcher, A. and Spitkovsky, I. M., A gentle guide to the basics of two projections theory. Linear Algebra Appl. 432 (2010), 1412–59.CrossRefGoogle Scholar
Boudi, N., On Jordan Banach algebras with countably generated inner ideals. Algebra Colloq. 17 (2010), 211–22. 601Google Scholar
Boudi, N., Marhnine, H., Zarhouti, C., Fernández, A., and García, E., Noetherian Banach Jordan pairs. Math. Proc. Cambridge Philos. Soc. 130 (2001), 2536. 601Google Scholar
Bouhya, K. and Fernández, A., Jordan-∗-triples with minimal inner ideals and compact JB -triples. Proc. London Math. Soc. 68 (1994), 380–98. 241, 461, 603Google Scholar
Boyko, K., Kadets, V., Martín, M., and Werner, D., Numerical index of Banach spaces and duality. Math. Proc. Cambridge Philos. Soc. 142 (2007), 93102.Google Scholar
Bratteli, O. and Robinson, D. W., Unbounded derivations of C -algebras. II. Comm. Math. Phys. 46 (1976), 1130.Google Scholar
Braun, R. B., Structure and representations of non-commutative C -Jordan algebras. Manuscripta Math. 41 (1983), 139–71. xx, xxi, 398, 411, 421Google Scholar
Braun, R. B., A Gelfand–Neumark theorem for C -alternative algebras. Math. Z. 185 (1984), 225–42. xx, xxi, 411Google Scholar
Braun, R. B., Kaup, W., and Upmeier, H., A holomorphic characterization of Jordan C -algebras. Math. Z. 161 (1978), 277–90. 210Google Scholar
Brelot, M., Points irréguliers et transformations continues en théorie du potentiel. J. Math. Pures Appl. 19 (1940), 319–37.Google Scholar
Brelot, M., Sur les ensembles effilés. Bull. Sci. Math. 68 (1944), 1236.Google Scholar
Bremner, M. and Hentzel, I., Identities for algebras obtained from the Cayley–Dickson process. Comm. Algebra 29 (2001), 3523–34.Google Scholar
Brešar, M., Cabrera, M., Fosner, M., and Villena, A. R., Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan–Banach algebras. Studia Math. 169 (2005), 207–28. 602Google Scholar
Brešar, M., Šemrl, P., and Špenko, S., On locally complex algebras and low-dimensional Cayley–Dickson algebras. J. Algebra 327 (2011), 107–25.Google Scholar
Browder, A., States, numerical ranges, etc.. In Proceedings of the Brown informal analysis seminar. Summer, 1969 (revised version, Summer of 2012).Google Scholar
Browder, A., On Bernstein’s inequality and the norm of Hermitian operators. Amer. Math. Monthly 78 (1971), 871–3.Google Scholar
Brown, R., On generalized Cayley–Dickson algebras. Pacific J. Math. 20 (1967), 415–22.Google Scholar
Bunce, L. J., Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., A Saitô–Tomita– Lusin theorem for JB -triples and applications. Quart. J. Math. Oxford 57 (2006), 3748.Google Scholar
Bunce, L. J. and Peralta, A. M., Images of contractive projections on operator algebras. J. Math. Anal. Appl. 272 (2002), 5566. 210CrossRefGoogle Scholar
Burgos, M. J., Peralta, A. M., Ramírez, M. I., and Ruiz, E. E., Von Neumann regularity in Jordan–Banach triples. In [704], pp. 67–88.Google Scholar
Busby, R. C., Double centralizers and extensions of C -algebras. Trans. Amer. Math. Soc. 132 (1968), 7999.Google Scholar
Cabello, F., Regards sur le problème des rotations de Mazur. Extracta Math. 12 (1997), 97116.Google Scholar
Cabrera, M., El Marrakchi, A., Martínez, J., and Rodríguez, A., An Allison– Kantor–Koecher–Tits construction for Lie H -algebras. J. Algebra 164 (1994), 361408. xxv, 556Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Malcev H -algebras. Math. Proc. Cambridge Phil. Soc. 103 (1988), 463–71. xxv, 553, 554Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Nonassociative real H -algebras. Publ. Mat. 32 (1988), 267–74. xxiv, 549, 551Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., A note on real H -algebras. Math. Proc. Cambridge Phil. Soc. 105 (1989), 131–2.CrossRefGoogle Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Structurable H -algebras. J. Algebra 147 (1992), 1962. xxv, 552, 553, 555, 556Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., Normed versions of the Zel’manov prime theorem: positive results and limits. In: Operator theory, operator algebras and related topics (Timisoara, 1996) (eds. Gheondea, A., Gologan, R. N. and Timotin, D.), Theta Found., Bucharest, 1997, pp. 6577. 462, 463, 465Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., Zel’manov’s theorem for primitive Jordan–Banach algebras. J. London Math. Soc. 57 (1998), 231–44. xxii, 463, 464, 465Google Scholar
Cabrera, M., Moreno, A., Rodríguez, A., and Zel’manov, E. I., Jordan polynomials can be analytically recognized. Studia Math. 117 (1996), 137–47. xxii, 437, 470Google Scholar
Cabrera, M. and Rodríguez, A., Extended centroid and central closure of semiprime normed algebras: a first approach. Comm. Algebra 18 (1990), 2293–326. xxiii, 408, 546, 555Google Scholar
Cabrera, M. and Rodríguez, A., Nonassociative ultraprime normed algebras. Quart. J. Math. Oxford 43 (1992), 17. xxi, xxiii, 409, 546Google Scholar
Cabrera, M. and Rodríguez, A., New associative and nonassociative Gelfand–Naimark theorems. Manuscripta Math. 79 (1993), 197208.Google Scholar
Cabrera, M. and Rodríguez, A., Zel’manov theorem for normed simple Jordan algebras with a unit. Bull. London Math. Soc. 25 (1993), 5963. xxii, 467, 468Google Scholar
Cabrera, M. and Rodríguez, A., Non-degenerately ultraprime Jordan–Banach algebras: a Zel’manovian treatment. Proc. London Math. Soc. 69 (1994), 576604. xxii, 409, 468, 469Google Scholar
Cabrera, M. and Rodríguez, A., A new simple proof of the Gelfand–Mazur–Kaplansky theorem. Proc. Amer. Math. Soc. 123 (1995), 2663–6. 408Google Scholar
Cabrera, M. and Rodríguez, A., On the Gelfand–Naimark axiom ‖a a‖ = ‖a ‖‖a. Quart. J. Math. Oxford 63 (2012), 855–60.Google Scholar
Calderón, A., Kaidi, A., Martín, C., Morales, A., Ramírez, M., and Rochdi, A., Finite-dimensional absolute-valued algebras. Israel J. Math. 184 (2011), 193220.Google Scholar
Calderón, A. J. and Martín, C., Two-graded absolute valued algebras. J. Algebra 292 (2005), 492515.Google Scholar
Calkin, J. W., Two-sided ideals and congruences in the ring of bounded operators in Hilbert space. Ann. of Math. 42 (1941), 839–73.Google Scholar
Caradus, S. R., Operators of Riesz type. Pacific J. Math. 18 (1966), 6171.Google Scholar
Cartan, E., Les groupes bilinéaires et les systèmes de nombres complexes. Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 12 (1898), 199. Reprinted in Oeuvres Complètes, Vol II, Paris, Gauthier-Villars, 1952.Google Scholar
Cartan, H., Théorie générale du balayage en potentiel newtonien. Ann. Univ. Grenoble. Sect. Sci. Math. Phys. 22 (1946), 221–80.Google Scholar
Casazza, P. G., Approximation properties. In Handbook of the geometry of Banach spaces, Vol. I (eds. Johnson, W. B. and Lindenstrauss, J.), pp. 271316, North-Holland, Amsterdam, 2001. Addenda and corrigenda: In [757], pp. 1817–18.Google Scholar
Castellón, A. and Cuenca, J. A., Isomorphisms of H -triple systems. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. 19 (1992), 507–14. 561Google Scholar
Castellón, A. and Cuenca, J. A., Associative H -triple systems. In [734], pp. 45–67. 551, 561Google Scholar
Cayley, A., On Jacobi’s elliptic functions, in reply to the Rev. B. Bronwin; and on quaternions. Philos. Mag. 26 (1845), 208–11.Google Scholar
Cedilnik, A. and Rodríguez, A., Continuity of homomorphisms into complete normed algebraic algebras. J. Algebra 264 (2003), 614. 595, 596Google Scholar
Cedilnik, A. and Zalar, B., Nonassociative algebras with submultiplicative bilinear form. Acta Math. Univ. Comenian. 63 (1994), 285301.Google Scholar
Chan, K.-C. and Dokovic, D. Z., Conjugacy classes of subalgebras of the real sedenions. Canad. Math. Bull. 49 (2006), 492507.Google Scholar
Chandid, A. and Rochdi, A., Mutations of absolute valued algebras. Int. J. Algebra 2 (2008), 357–68.Google Scholar
Choi, M. D. and Effros, E., Injectivity and operator spaces. J. Funct. Anal. 24 (1974), 156209.Google Scholar
Chonghu, W., Some geometric properties of Banach spaces and x+λy‖−‖x λ on it. J. Nanjing Univ. 6 (1989), 3745.Google Scholar
Chu, C.-H., Dang, T., Russo, B., and Ventura, B., Surjective isometries of real C -algebras. J. London Math. Soc. 47 (1993), 97118.Google Scholar
Chu, C.-H., Iochum, B., and Loupias, G., Grothendieck’s theorem and factorization of operators in Jordan triples. Math. Ann. 284 (1989), 4153. xix, 2, 245, 267, 343, 344, 346Google Scholar
Chu, C.-H. and Mellon, P., Jordan structures in Banach spaces and symmetric manifolds. Expos. Math. 16 (1998), 157–80. 211Google Scholar
Chu, C.-H. and Velasco, M. V., Automatic continuity of homomorphisms in nonassociative Banach algebras. Canadian J. Math. 65 (2013), 9891004.Google Scholar
Civin, P. and Yood, B., Lie and Jordan structures in Banach algebras. Pacific J. Math. 15 (1965), 775–97. 583Google Scholar
Cleveland, S. B., Homomorphisms of non-commutative ∗-algebras. Pacific J. Math. 13 (1963), 1097–109.Google Scholar
Cobalea, M. A. and Fernández, A., Prime noncommutative Jordan algebras and central closure. Algebras Groups Geom. 5 (1988), 129–36. 408Google Scholar
Cohn, P. M., On homomorphic images of special Jordan algebras. Canadian J. Math. 6 (1954), 253–64.Google Scholar
Contreras, M. D. and Payá, R., On upper semicontinuity of duality mappings. Proc. Amer. Math. Soc. 121 (1994), 451–9.Google Scholar
Contreras, M. D., Payá, R., and Werner, W., C -algebras that are I-rings. J. Math. Anal. Appl. 198 (1996), 227–36.Google Scholar
Cowie, E. R., An analytic characterization of groups with no finite conjugacy classes. Proc. Amer. Math. Soc. 87 (1983), 710.Google Scholar
Crabb, M. J., Duncan, J., and McGregor, C. M., Some extremal problems in the theory of numerical ranges. Acta Math. 128 (1972), 123–42.Google Scholar
Crabb, M. J., Duncan, J., and McGregor, C. M., Characterizations of commutativity for C -algebras. Glasgow Math. J. 15 (1974), 172–5. 400Google Scholar
Crabb, M. J. and McGregor, C. M., Numerical ranges of powers of Hermitian elements. Glasgow Math. J. 28 (1986), 3745.Google Scholar
Crabb, M. J. and McGregor, C. M., Polynomials in a Hermitian element. Glasgow Math. J. 30 (1988), 171–6.Google Scholar
Cuartero, B. and Galé, J. E., Locally PI-algebras over valued fields. In Aportaciones Matemáticas en Memoria del Profesor V. M. Onieva, pp. 137–45, Santander, Universidad de Cantabria, 1991.Google Scholar
Cuartero, B. and Galé, J. E., Bounded degree of algebraic topological algebras. Comm. Algebra 422 (1994), 329–37.Google Scholar
Cuartero, B., Galé, J. E., Rodríguez, A., and Slinko, A. M., Bounded degree of weakly algebraic topological Lie algebras. Manuscripta Math. 81 (1993), 129–39. 658Google Scholar
Cudia, D. F., The geometry of Banach spaces. Smoothness. Trans. Amer. Math. Soc. 110 (1964), 284314.Google Scholar
Cuenca, J. A., On one-sided division infinite-dimensional normed real algebras. Publ. Mat. 36 (1992), 485–8.Google Scholar
Cuenca, J. A., On composition and absolute-valued algebras. Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), 717–31.Google Scholar
Cuenca, J. A., On an Ingelstam’s theorem. Comm. Algebra 35 (2007), 4057–67.Google Scholar
Cuenca, J. A., On structure theory of pre-Hilbert algebras. Proc. R. Soc. Edinburgh 139A (2009), 303–19.Google Scholar
Cuenca, J. A., Some classes of pre-Hilbert algebras with norm-one central idempotent. Israel J. Math. 193 (2013), 343–58.Google Scholar
Cuenca, J. A., A new class of division algebras and Wedderburn’s and Frobenius’ Theorems. Preprint 2012.Google Scholar
Cuenca, J. A., Third-power associative absolute vaued algebras with a nonzero idempotent commuting with all idempotents. Publ. Mat. 58 (2014), 469–84.Google Scholar
Cuenca, J. A., García, A., and Martín, C.. Structure theory for L -algebras, Math. Proc. Cambridge Phil. Soc. 107 (1990), 361–5. xxv, 554Google Scholar
Cuenca, J. A. and Rodríguez, A., Isomorphisms of H -algebras. Math. Proc. Cambridge Phil. Soc. 97 (1985), 93–9. xxiv, 546, 549Google Scholar
Cuenca, J. A. and Rodríguez, A., Structure theory for noncommutative Jordan H -algebras. J. Algebra 106 (1987), 114. xxiii, xxv, 545, 552, 553Google Scholar
Cuenca, J. A. and Rodríguez, A., Absolute values on H -algebras. Comm. Algebra 23 (1995), 1709–40. 481Google Scholar
Cuntz, J., Locally C -equivalent algebras. J. Funct. Anal. 23 (1976), 95106.Google Scholar
Cusack, J. M., Jordan derivations on rings. Proc. Amer. Math. Soc. 53 (1975), 321–4.Google Scholar
Dales, H. G., Norming nil algebras. Proc. Amer. Math. Soc. 83 (1981), 71–4.Google Scholar
Dales, H. G., On norms on algebras. In [773], pp. 61–96.Google Scholar
Dang, T., Real isometries between JB -triples. Proc. Amer. Math. Soc. 114 (1992), 971–80.Google Scholar
Dang, T. and Russo, B., Real Banach Jordan triples. Proc. Amer. Math. Soc. 122 (1994), 135–45.Google Scholar
Darpö, E. and Rochdi, A., Classification of the four-dimensional power-commutative real division algebras. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), 1207–23.Google Scholar
Davis, W. J., Separable Banach spaces with only trivial isometries. Rev. Roumaine Math. Pures Appl. 16 (1971), 1051–4.Google Scholar
Davis, W. J., Figiel, T., Johnson, W. B., and Pełczyński, A., Factoring weakly compact operators. J. Funct. Anal. 17 (1974), 311–27.Google Scholar
Diankha, O., Diouf, A., and Rochdi, A., A brief statement on the absolute-valued algebras with one-sided unit. Int. J. Algebra 7 (2013), 833–8.Google Scholar
Dickson, L. E., On quaternions and their generalization and the history of the eight square theorem. Ann. of Math. 20 (1919), 155–71.Google Scholar
Dickson, L. E., Linear algebras with associativity not assumed. Duke Math. J. 1 (1935), 113–25.Google Scholar
Dineen, S., The second dual of a JB -triple system. In Complex Analysis, Functional Analysis and Approximation Theory (ed. Múgica, J.), pp. 67–9, North-Holland Math. Stud. 125, North-Holland, Amsterdam–New York, 1986. xix, 2, 211, 236, 241Google Scholar
Doran, R. S., A generalization of a theorem of Civin and Yood on Banach ∗-algebras. Bull. London Math. Soc. 4 (1972), 25–6.Google Scholar
Dorofeev, G. V., An example of a solvable but not nilpotent alternative ring. Uspekhi Mat. Nauk 15 (1960), 147–50.Google Scholar
Duncan, J., Review of [425]. Math. Rev. 87e:46067.Google Scholar
Duncan, J., McGregor, C. M., Pryce, J. D., and White, A. J., The numerical index of a normed space. J. London Math. Soc. 2 (1970), 481–8.Google Scholar
Duncan, J. and Taylor, P. J., Norm inequalities for C -algebras. Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), 119–29. 400Google Scholar
Dunford, N., Spectral theory I. Convergence to projections. Trans. Amer. Math. Soc. 54 (1943), 185217.Google Scholar
Dutta, S. and Rao, T. S. S. R. K., Norm-to-weak upper semi-continuity of the pre-duality map. J. Anal. 12 (2005), 110.Google Scholar
Eakin, P. and Sathaye, A., On automorphisms and derivations of Cayley–Dickson algebras. J. Algebra 129 (1990), 263–78.Google Scholar
Edwards, C. M., On Jordan W -algebras. Bull. Sci. Math. 104 (1980), 393403. xix, xx, 2, 19Google Scholar
Edwards, C. M., Multipliers of JB-algebras. Math. Ann. 249 (1980), 265–72.Google Scholar
Edwards, C. M., Fernández-Polo, F. J., Hoskin, C. S., and Peralta, A. M., On the facial structure of the unit ball in a JB -triple. J. Reine Angew. Math. 641 (2010), 123–44.Google Scholar
Edwards, C. M. and Rüttimann, G. T., On the facial structure of the unit balls in a JBW -triple and its predual. J. London Math. Soc. 38 (1988), 317–32.Google Scholar
Edwards, C. M. and Rüttimann, G. T., The facial and inner ideal structure of a real JBW -triple. Math. Nachr. 222 (2001), 159–84.Google Scholar
Edwards, R. E., Multiplicative norms on Banach algebras. Math. Proc. Cambridge Phil. Soc. 47 (1951), 473–4.Google Scholar
Effros, E. G. and Størmer, E., Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc. 127 (1967), 313–16.Google Scholar
Effros, E. G. and Størmer, E., Positive projections and Jordan structure in operator algebras. Math. Scand. 45 (1979), 127–38. 210Google Scholar
Eidelheit, M., On isomorphisms of rings of linear operators. Studia Math. 9 (1940), 97105.Google Scholar
Eilenberg, S., Extensions of general algebras. Ann. Soc. Polon. Math. 21 (1948), 125–34.Google Scholar
Elduque, A. and Pérez, J. M., Infinite-dimensional quadratic forms admitting composition. Proc. Amer. Math. Soc. 125 (1997), 2207–16.Google Scholar
Ellis, A. J., The duality of partially ordered normed linear spaces. J. London Math. Soc. 39 (1964), 730–44.Google Scholar
Ellis, A. J., Minimal decompositions in base normed spaces. In Foundations of quantum mechanics and ordered linear spaces (Advanced Study Inst., Marburg, 1973), pp. 30–2. Lecture Notes in Phys. 29, Springer, Berlin, 1974.Google Scholar
El-Mallah, M. L., Quelques résultats sur les algèbres absolument valuées. Arch. Math. 38 (1982), 432–7.Google Scholar
El-Mallah, M. L., Sur les algèbres absolument valuées qui vérifient l’identité (x, x, x)=0. J. Algebra 80 (1983), 314–22.Google Scholar
El-Mallah, M. L., On finite dimensional absolute valued algebras satisfying (x, x, x)=0. Arch. Math. 49 (1987), 1622.Google Scholar
El-Mallah, M. L., Absolute valued algebras with an involution. Arch. Math. 51 (1988), 3949.Google Scholar
El-Mallah, M. L., Absolute valued algebras containing a central idempotent. J. Algebra 128 (1990), 180–7.Google Scholar
El-Mallah, M. L., Absolute valued algebraic algebra satisfying (x, x, x) = 0. Pure Math. Appl. 8 (1997), 3952.Google Scholar
El-Mallah, M. L., Semi-algebraic absolute valued algebras with an involution. Comm. Algebra 31 (2003), 3135–41.Google Scholar
El-Mallah, M. L., Elgendy, H., Rochdi, A., and Rodríguez, A., On absolute valued algebras with involution. Linear Algebra Appl. 414 (2006), 295303.Google Scholar
El-Mallah, M. L. and Micali, A., Sur les algèbres normées sans diviseurs topologiques de zéro. Bol. Soc. Mat. Mexicana 25 (1980), 23–8.Google Scholar
El-Mallah, M. L. and Micali, A., Sur les dimensions des algèbres absolument valuées. J. Algebra 68 (1981), 237–46.Google Scholar
Enflo, P., A counterexample to the approximation problem in Banach spaces. Acta Math. 130 (1973), 309–17.Google Scholar
Erickson, T. S., Martindale, W. S. III, and Osborn, J. M., Prime nonassociative algebras. Pacific J. Math. 60 (1975), 4963. 495Google Scholar
Esterle, J., Normes d’algèbres minimales, topologie d’algèbre normée minimum sur certaines algèbres d’endomorphismes continus d’un espace normé. C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A425–7.Google Scholar
Fan, K. and Glicksberg, I., Some geometrical properties of the spheres in a normed linear space. Duke Math. J. 25 (1958), 553–68.Google Scholar
Feldman, K. E., New proof of Frobenius hypothesis on the dimensions of real algebras without divisors of zero. Moscow Univ. Math. Bull. 55 (2000), 4850.Google Scholar
Fernández, A., Modular annihilator Jordan algebras. Comm. Algebra 13 (1985), 2597–613. 598Google Scholar
Fernández, A., Noncommutative Jordan Riesz algebras. Quart. J. Math. Oxford 39 (1988), 6780. 598, 599Google Scholar
Fernández, A., Noncommutative Jordan algebras containing minimal inner ideals. In [749], pp. 153–76.Google Scholar
Fernández, A., Banach–Lie algebras spanned by extremal elements. In [704], pp. 125–32. 598Google Scholar
Fernández, A., Banach–Lie algebras with extremal elements. Quart. J. Math. Oxford 62 (2011), 115–29. 598Google Scholar
Fernández, A., García, E., and Rodríguez, A., A Zel’manov prime theorem for JB -algebras. J. London Math. Soc. 46 (1992), 319–35. xxi, xxii, 405, 408, 437, 466, 467Google Scholar
Fernández, A., García, E., and Sánchez, E., von Neumann regular Jordan Banach triple systems. J. London Math. Soc. 42 (1990), 3248. 599, 600Google Scholar
Fernández, A. and Rodríguez, A., Primitive noncommutative Jordan algebras with nonzero socle. Proc. Amer. Math. Soc. 96 (1986), 199206. 598Google Scholar
Fernández, A. and Rodríguez, A., On the socle of a noncommutative Jordan algebra. Manuscripta Math. 56 (1986), 269–78. 598Google Scholar
Fernández, A. and Rodríguez, A., A Wedderburn theorem for nonassociative complete normed algebras. J. London Math. Soc. 33 (1986), 328–38. xxv, 548, 583, 584, 585Google Scholar
Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., Surjective isometries between real JB -triples. Math. Proc. Cambridge Phil. Soc. 137 (2004), 709–23.Google Scholar
Fernández-Polo, F. J., Martínez, J., and Peralta, A. M., Geometric characterization of tripotents in real and complex JB -triples. J. Math. Anal. Appl. 295 (2004), 435–43.Google Scholar
Fernández-Polo, F. J., Garcés, J. J., and Peralta, A. M., A Kaplansky theorem for JB -triples. Proc. Amer. Math. Soc. 140 (2012), 3179–91.Google Scholar
Finet, C., Uniform convexity properties of norms on superreflexive Banach spaces. Israel J. Math. 53 (1986), 8192.Google Scholar
Foias, C., Sur certains theoremes de J. von Neumann concernant les ensembles spectraux. Acta Sci. Math. 18 (1957), 1520.Google Scholar
Ford, J. W. M., A square root lemma for Banach ∗-algebras. J. London Math. Soc. 42 (1967), 521–2.Google Scholar
Formanek, E., The Nagata–Higman Theorem. Acta Appl. Math. 21 (1990), 185–92.Google Scholar
Franchetti, C., Lipschitz maps and the geometry of the unit ball in normed spaces. Arch. Math. 46 (1986), 7684.Google Scholar
Franchetti, C. and Payá, R., Banach spaces with strongly subdifferentiable norm. Boll. Un. Mat. Ital. 7 (1993), 4570.Google Scholar
Friedman, Y. and Russo, B., Structure of the predual of a JBW -triple. J. Reine Angew. Math. 356 (1985), 6789. 236, 274, 332, 337Google Scholar
Friedman, Y. and Russo, B., The Gelfand–Naimark theorem for JB -triples. Duke Math. J. 53 (1986), 139–48. xxii, 459Google Scholar
Frobenius, F. G., Über lineare Substitutionen und bilineare Formen. J. Reine Angew. Math. 84 (1878), 163. Reprinted in Gesammelte Abhandlungen Band I, pp. 343–405.Google Scholar
Froelich, J., Unital multiplications on a Hilbert space. Proc. Amer. Math. Soc. 117 (1993), 757–9.Google Scholar
Fukamiya, M., On a theorem of Gelfand and Neumark and the B -algebra. Kumamoto J. Sci. Ser. A 1 (1952), 1722. 686Google Scholar
Fuster, R. and Marquina, A., Geometric series in incomplete normed algebras. Amer. Math. Monthly 91 (1984), 4951.Google Scholar
Galé, J. E., Weakly compact homomorphisms in nonassociative algebras. In [734], pp. 167–71.Google Scholar
Galé, J. E., Ransford, T. J., and White, M. C., Weakly compact homomorphisms. Trans. Amer. Math. Soc. 331 (1992), 815–24. 336Google Scholar
Galina, E., Kaplan, A., and Saal, L., Charged representations of the infinite Fermi and Clifford algebras. Lett. Math. Phys. 72 (2005), 6577.Google Scholar
Galina, E., Kaplan, A., and Saal, L., Spinor types in infinite dimensions. J. Lie Theory 15 (2005), 457–95.Google Scholar
Gantmacher, V., Über schwache totalstetige Operatoren. Rec. Math. [Mat. Sbornik] 7 (1940), 301–8.Google Scholar
Gardner, L. T., On isomorphisms of C -algebras. Amer. J. Math. 87 (1965), 384–96.Google Scholar
Gardner, L. T., An elementary proof of the Russo–Dye theorem. Proc. Amer. Math. Soc. 90 (1984), 181.Google Scholar
Garibaldi, S. and Petersson, H. P., Wild Pfister forms over Henselian fields, K-theory, and conic division algebras. J. Algebra 327 (2011), 386465.Google Scholar
Gelfand, I. M., Abstrakte Funktionen und lineare Operatoren, Mat. Sb. 4 (1938), 235–86.Google Scholar
Gelfand, I. M., Normierte Ringe. Rec. Math. [Mat. Sbornik]9 (1941), 324.Google Scholar
Gelfand, I. M. and Naimark, M. A., On the embedding of normed rings into the ring of operators in Hilbert space. Mat. Sbornik 12 (1943), 197213.Google Scholar
Gelfand, I. M. and Kolmogorov, A. N., Rings of continuous functions on topological spaces. Doklady Akad. Nauk SSSR 22 (1939), 1115.Google Scholar
Giles, J. R., Gregory, D. A., and Sims, B., Geometrical implications of upper semi-continuity of the duality mapping of a Banach space. Pacific J. Math. 79 (1978), 99109.Google Scholar
Gleichgewicht, B., A remark on absolute-valued algebras. Colloq. Math. 11 (1963), 2930.Google Scholar
Glickfeld, B. W., A metric characterization of C(X) and its generalization to C -algebras. Illinois J. Math. 10 (1966), 547–56.Google Scholar
Glimm, J. G. and Kadison, R. V., Unitary operators in C -algebras. Pacific J. Math. 10 (1960), 547–56.Google Scholar
Godefroy, G. and Indumathi, V., Norm-to-weak upper semi-continuity of the duality and pre-duality mappings. Set-Valued Anal. 10 (2002), 317–30.Google Scholar
Godefroy, G., Montesinos, V., and Zizler, V., Strong subdifferentiability of norms and geometry of Banach spaces. Comment. Math. Univ. Carolinae 36 (1995), 493502.Google Scholar
Godefroy, G. and Rao, T. S. S. R. K., Renorming and extremal structures. Illinois J. Math. 48 (2004), 1021–9.Google Scholar
Gohberg, I. C., Markus, A. S., and Fel’dman, I. A., Normally solvable operators and ideals associated with them. Bul. Akad. Stiince RSS Moldoven 10 (1960), 5170. Amer. Math. Soc. Transl. 61 (1967), 63–4.Google Scholar
Golod, E. S., On nil-algebras and finitely approximable p-groups. Izv. Akad. Nauk SSSR, Ser. Mat. 28 (1964), 273–6. 633Google Scholar
Gorin, E. A., Bernstein inequalities from the perspective of operator theory. (In Russian.) Vestnik Khar’kov. Gos. Univ. 205 (1980), 77105, 140.Google Scholar
Gowers, W. T. and Maurey, B., The unconditional basic sequence problem. J. Amer. Math. Soc. 6 (1993), 851–74.Google Scholar
Grabiner, S., The nilpotence of Banach nil algebras. Proc. Amer. Math. Soc. 21 (1969), 510.Google Scholar
Gregory, D. A., Upper semi-continuity of subdifferential mappings. Canad. Math. Bull. 23 (1980), 1119.Google Scholar
Greim, P. and Rajalopagan, M., Almost transitivity in C 0(L). Math. Proc. Cambridge Phil. Soc. 121 (1997), 7580.Google Scholar
Grzaślewicz, R. and Scherwentke, P., On strongly extreme and denting contractions in L (C(X), C(Y)). Bull. Acad. Sinica 25 (1997), 155–60.Google Scholar
Haagerup, U., Kadison, R. V., and Pedersen, G. K., Means of unitary operators, revisited. Math. Scand. 100 (2007), 193–7.Google Scholar
Haïly, A., A non-semiprime associative algebra with zero weak radical. Extracta Math. 12 (1997), 5360.Google Scholar
Haïly, A., Kaidi, A., and Rodríguez, A., Algebra descent spectrum of operators. Israel J. Math. 177 (2010), 349–68.Google Scholar
Hamana, M., Injective envelopes of C -algebras. J. Math. Soc. Japan 31 (1979), 181–97.Google Scholar
Hamilton, W. R., Note by Professor Sir W. R. Hamilton, respecting the researches of John T. Graves, esq. Trans. R. Irish Acad., 1848, Science 338–41.Google Scholar
Hammoudi, L., Nil-algebras and infinite groups. J. Math. Sci. (NY) 144 (2007), 4004–12.Google Scholar
Hanche-Olsen, H., A note on the bidual of a JB-algebra. Math. Z. 175 (1980), 2931.Google Scholar
Hansen, M. L. and Kadison, R. V., Banach algebras with unitary norms. Pacific J. Math. 175 (1996), 535–52.Google Scholar
Hansen, F. and Pedersen, G. K., Jensen’s inequality for operators and Löwner’s theorem. Math. Ann. 258 (1981/82), 229–41.Google Scholar
Harmand, P. and Rao, T. S. S. R. K., An intersection property of balls and relations with M-ideals. Math. Z. 197 (1988), 277–90.Google Scholar
Harris, L. A., The numerical range of holomorphic functions in Banach spaces. Amer. J. Math. 93 (1971), 1005–19.Google Scholar
Harris, L. A., Banach algebras with involution and Möbius transformations. J. Funct. Anal. 11 (1972), 116.Google Scholar
Harris, L. A., Bounded symmetric homogeneous domains in infinite dimensional spaces. In Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973), pp. 1340. Lecture Notes in Math. 364, Springer, Berlin, 1974. 210, 211Google Scholar
Harris, L. A., The numerical range of functions and best approximation. Math. Proc. Cambridge Philos. Soc. 76 (1974), 133–41.Google Scholar
Harris, L. A. and Kadison, R. V., Schurian algebras and spectral additivity. J. Algebra 180 (1996), 175–86.Google Scholar
Harte, R. and Mbekhta, M., On generalized inverses in C -algebras. Studia Math. 103 (1992), 71–7.Google Scholar
Heinrich, S., Ultraproducts in Banach space theory. J. Reine Angew. Math. 313 (1980), 72104. 211, 236Google Scholar
Hejazian, S. and Niknam, A., A Kaplansky theorem for JB -algebras. Rocky Mountain J. Math. 28 (1998), 977–82.Google Scholar
Herstein, I. N., Jordan homomorphism. Trans. Amer. Math. Soc. 81 (1956), 331–41.Google Scholar
Herstein, I. N., Jordan derivations of prime rings. Proc. Amer. Math. Soc. 8 (1957), 1104–10.Google Scholar
Hessenberger, G., A spectral characterization of the socle of Banach Jordan systems. Math. Z. 223 (1996), 561–8. 603Google Scholar
Hessenberger, G., Inessential and Riesz elements in Banach Jordan systems. Quart. J. Math. Oxford 47 (1996), 337–47. 603Google Scholar
Hessenberger, G., The trace in Banach Jordan pairs. Bull. London Math. Soc. 30 (1998), 561–8. 603Google Scholar
Hessenberger, G., An improved characterization of inessential elements in Banach Jordan systems and the generalized Ruston characterization. Arch. Math. (Basel) 74 (2000), 438–40. 603Google Scholar
Hessenberger, G. and Maouche, A., On Banach Jordan systems with at most two spectral values. Far East J. Math. Sci. (FJMS) 7 (2002), 115–20. 603Google Scholar
Hirschfeld, R. A. and Johnson, B. E., Spectral characterization of finite-dimensional algebras. Indag. Math. 34 (1972), 1923. 596Google Scholar
Hogben, L. and McCrimmon, K., Maximal modular inner ideals and the Jacobson radical of a Jordan algebra. J. Algebra 68 (1981), 155–69.Google Scholar
Holsztynski, W., Continuous mappings induced by isometries of spaces of continuous functions. Studia Math. 26 (1966), 133–6.Google Scholar
Horn, G., Classification of JBW -triples of Type I. Math. Z. 196 (1987), 271–91. xxii, 340, 344, 438, 459Google Scholar
Horn, G., Coordinatization theorem for JBW -triples. Quart. J. Math. Oxford 38 (1987), 321–35. xxi, 411, 416Google Scholar
Huang, X.-J. and Ng, C.-K., An abstract characterization of unital operator spaces. J. Operator Theory 67 (2012), 289–98.Google Scholar
Huruya, T., The normed space numerical index of C -algebras. Proc. Amer. Math. Soc. 63 (1977), 289–90.Google Scholar
Hurwitz, A., Über die Composition der quadratischen Formen von beliebig vielen Variabelm. Nach. Ges. Wiss. Göttingen (1898), 309–16.Google Scholar
Imaeda, K. and Imaeda, M., Sedenions: algebra and analysis. Appl. Math. Comp. 115 (2000), 7788.Google Scholar
Ingelstam, L., A vertex property for Banach algebras with identity, Math. Scand. 11 (1962), 2232.Google Scholar
Ingelstam, L., Hilbert algebras with identity. Bull. Amer. Math. Soc. 69 (1963), 794–6.Google Scholar
Ingelstam, L., Non-associative normed algebras and Hurwitz’ problem. Ark. Mat. 5 (1964), 231–8.Google Scholar
Ingelstam, L., Real Banach algebras. Ark. Mat. 5 (1964), 239–79.Google Scholar
Iochum, B., Loupias, G, and Rodríguez, A., Commutativity of C -algebras and associativity of JB -algebras. Math. Proc. Cambridge Phil. Soc. 106 (1989), 281–91. xxi, 398, 399, 400, 401Google Scholar
Isidro, J. M., Kaup, W., and Rodríguez, A., On real forms of JB -triples. Manuscripta Math. 86 (1995), 311–35. 242, 243, 459Google Scholar
Isidro, J. M. and Rodríguez, A., Isometries of JB-algebras. Manuscripta Math. 86 (1995), 337–48.Google Scholar
Isidro, J. M. and Rodríguez, A., On the definition of real W*-algebras. Proc. Amer. Math. Soc. 124 (1996), 3407–10. 244Google Scholar
Jacobson, N., Structure theory of simple rings without finiteness assumptions. Trans. Amer. Math. Soc. 57 (1945), 228–45.Google Scholar
Jacobson, N., The radical and semisimplicity for arbitrary rings. Amer. J. Math. 67 (1945), 300–20.Google Scholar
Jacobson, N., A topology for the set of primitive ideals in an arbitrary ring. Proc. Nat. Acad. Sci. USA 31 (1945), 333–8.Google Scholar
Jacobson, N., Structure theory for algebraic algebras of bounded degree. Ann. of Math. 46 (1945), 695707.Google Scholar
Jacobson, N., A theorem on the structure of Jordan algebras. Proc. Nat. Acad. Sci. USA 42 (1956), 140–7.Google Scholar
Jacobson, N., Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo 7 (1958), 5580.Google Scholar
Jacobson, N., Abraham Adrian Albert 1905–1972. Bull. Amer. Math. Soc. 80 (1974), 1075–100. Reprinted in [691], pp. xlv–lxiii. 546Google Scholar
Jacobson, N. and Rickart, C. E., Jordan homomorphisms of rings. Trans. Amer. Math. Soc. 69 (1950), 479502.Google Scholar
Johnson, B. E., Centralisers on certain topological algebras. J. London Math. Soc. 39 (1964), 603–14.Google Scholar
Johnson, B. E., The uniqueness of the (complete) norm topology. Bull. Amer. Math. Soc. 73 (1967), 537–9. 596Google Scholar
Johnson, B. E., Continuity of derivations on commutative Banach algebras. Amer. J. Math. 91 (1969), 110.Google Scholar
Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky. Amer. J. Math. 90 (1968), 1067–73. 466, 548, 596Google Scholar
Jordan, P., von Neumann, J., and Wigner, E., On an algebraic generalization of the quantum mechanical formalism. Ann. of Math. 35 (1934), 2964.Google Scholar
Kadets, V., Katkova, O., Martín, M., and Vishnyakova, A., Convexity around the unit of a Banach algebra. Serdica Math. J. 34 (2008), 619–28.Google Scholar
Kadison, R. V., Isometries of operator algebras. Ann. of Math. 54 (1951), 325–38.Google Scholar
Kadison, R. V., A generalized Schwarz inequality and algebraic invariants for operator algebras. Ann. of Math. 56 (1952), 494503.Google Scholar
Kadison, R. V. and Pedersen, G. K., Means and convex combinations of unitary operators. Math. Scand. 57 (1985), 249–66.Google Scholar
Kaidi, A., Structure des algèbres de Jordan–Banach non commutatives reelles de division. In [749], pp. 119–24. 597Google Scholar
Kaidi, A., Martínez, J., and Rodríguez, A., On a non-associative Vidav–Palmer theorem. Quart. J. Math. Oxford 32 (1981), 435–42.Google Scholar
Kaidi, A., Morales, A, and Rodríguez, A., Prime non-commutative JB -algebras. Bull. London Math. Soc. 32 (2000), 703–8. xxii, 421Google Scholar
Kaidi, A., Morales, A., and Rodríguez, A., Geometrical properties of the product of a C -algebra. Rocky Mountain J. Math. 31 (2001), 197213.Google Scholar
Kaidi, A., Morales, A, and Rodríguez, A., A holomorphic characterization of C - and JB -algebras. Manuscripta Math. 104 (2001), 467–78. xviii, 272, 273Google Scholar
Kaidi, A., Morales, A., and Rodríguez, A., Non-associative C -algebras revisited. In [1141], pp. 379–408. xx, 275, 330, 346, 421, 422Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Absolute-valued algebraic algebras are finite-dimensional. J. Algebra 195 (1997), 295307.Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Absolute-valued algebraic algebras. In [705], pp. 103–9.Google Scholar
Kaidi, A., Ramírez, M. I., and Rodríguez, A., Nearly absolute-valued algebras. Comm. Algebra 30 (2002), 3267–84.Google Scholar
Kaidi, A. and Sánchez, A., J-diviseurs topologiques de zéro dans une algèbre de Jordan n.c. normée. In [733], pp. 193–7. 597Google Scholar
Kamowitz, H. and Scheinberg, S., The spectrum of automorphisms of Banach algebras. J. Funct. Anal. 4 (1969), 268–76.Google Scholar
Kaplansky, I., Topological rings. Amer. J. Math. 69 (1947), 153–83.Google Scholar
Kaplansky, I., Topological methods in valuation theory. Duke Math. J. 14 (1947), 527–41.Google Scholar
Kaplansky, I., Dual rings. Ann. of Math. 49 (1948), 689701. xxv, 551, 584Google Scholar
Kaplansky, I., Normed algebras. Duke Math. J. 16 (1949), 399418. 584Google Scholar
Kaplansky, I., Topological representation of algebras II. Trans. Amer. Math. Soc. 68 (1950), 6275.Google Scholar
Kaplansky, I., Infinite-dimensional quadratic forms permitting composition. Proc. Amer. Math. Soc. 4 (1953), 956–60. 360Google Scholar
Kaplansky, I., Ring isomorphisms of Banach algebras. Canad. J. Math. 6 (1954), 374–81. 596, 597Google Scholar
Kaplansky, I., ‘Problems in the theory of rings’ revisited. Amer. Math. Monthly 77 (1970), 445–54.Google Scholar
Kaup, W., Algebraic characterization of symmetric complex Banach manifolds. Math. Ann. 228 (1977), 3964. 2, 209, 210, 211, 241Google Scholar
Kaup, W., A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z. 183 (1983), 503–29. xix, 2, 209, 210, 211, 241Google Scholar
Kaup, W., Contractive projections on Jordan C -algebras and generalizations. Math. Scand. 54 (1984), 95100. xix, 207, 210Google Scholar
Kaup, W., On real Cartan factors. Manuscripta Math. 92 (1997), 191222. 460Google Scholar
Kaup, W., JB -triple. In [741], pp. 218–19. 462Google Scholar
Kaup, W. and Upmeier, H., Jordan algebras and symmetric Siegel domains in Banach spaces. Math. Z. 157 (1977), 179200. 211Google Scholar
Kawamura, K., On a conjecture of Wood. Glasgow Math. J. 47 (2005), 15.Google Scholar
Kelley, J. L. and Vaught, R. L., The positive cone in Banach algebras. Trans. Amer. Math. Soc. 74 (1953), 4455.Google Scholar
Kervaire, M., Non-parallelizability of the n sphere for n > 7. Proc. Nat. Acad. Sci. USA 44 (1958), 280–3.Google Scholar
Kleinecke, D. C., On operator commutators. Proc. Amer. Math. Soc. 8 (1957), 535–6.Google Scholar
Kleinfeld, E., Primitive alternative rings and semi-simplicity. Amer. J. Math. 77 (1955), 725–30. 570Google Scholar
Koliha, J. J., Isolated spectral points. Proc. Amer. Math. Soc. 124 (1996), 3417–24.Google Scholar
Koszmider, P., Martín, M., and Merí, J., Isometries on extremely non-complex Banach spaces. J. Inst. Math. Jussieu 10 (2011), 325–48.Google Scholar
Krupnik, N., Roch, S., and Silbermann, B., On C -algebras generated by idempotents. J. Funct. Anal. 137 (1996), 303–19.Google Scholar
Kulkarni, S. H., A very simple and elementary proof of a theorem of Ingelstam. Amer. Math. Monthly 111 (2004), 54–8.Google Scholar
Kunen, K. and Rosenthal, H., Martingale proofs of some geometrical results in Banach space theory. Pacific J. Math. 100 (1982), 153–75.Google Scholar
Kurosch, A., Ringtheoretische Probleme, die mit dem Burnsideschen Problem über periodische Gruppen in Zusammenhang stehen. Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 5 (1941), 233–40.Google Scholar
Kuwata, S., Born–Infeld Lagrangian using Cayley–Dickson algebras. Internat. J. Modern Physics A 19 (2004), 1525–48.Google Scholar
Laustsen, N. J., On ring-theoretic (in)finiteness of Banach algebras of operators on Banach spaces. Glasgow Math. J. 45 (2003), 1119.Google Scholar
Leung, C.-W., Ng, C.-K., and Wong, N.-C., Geometric unitaries in JB-algebras. J. Math. Anal. Appl. 360 (2009), 491–4.Google Scholar
Lima, Å., The metric approximation property, norm-one projections and intersection properties of balls. Israel J. Math. 84 (1993), 451–75.Google Scholar
Loos, O., Fitting decomposition in Jordan systems. J. Algebra 136 (1991), 92102.Google Scholar
Loos, O., Properly algebraic and spectrum-finite ideals in Jordan systems. Math. Proc. Cambridge Philos. Soc. 114 (1993), 149–61. 600Google Scholar
Loos, O., On the set of invertible elements in Banach Jordan algebras. Results Math. 29 (1996), 111–14. 597Google Scholar
Loos, O., Trace and norm for reduced elements of Jordan pairs. Comm. Algebra 25 (1997), 3011–42. 601Google Scholar
Loos, O., Nuclear elements in Banach Jordan pairs. In [705], pp. 111–17. 601Google Scholar
Loy, R. J., Maximal ideal spaces of Banach algebras of derivable elements. J. Austral. Math. Soc. 11 (1970), 310–12.Google Scholar
Lumer, G., Semi-inner-product spaces. Trans. Amer. Math. Soc. 100 (1961), 2943.Google Scholar
Lumer, G., Complex methods, and the estimation of operator norms and spectra from real numerical ranges. J. Funct. Anal. 10 (1972), 482–95.Google Scholar
Lumer, G. and Phillips, R. S., Dissipative operators in a Banach space. Pacific J. Math. 11 (1961), 679–98. 208Google Scholar
Macdonald, I. G., Jordan algebras with three generators. Proc. London Math. Soc. 10 (1960), 395408.Google Scholar
Magajna, B., Weak* continuous states on Banach algebras. J. Math. Anal. Appl. 350 (2009), 252–5.Google Scholar
Maouche, A., Caractérisations spectrales du radical et du socle d’une paire de Jordan–Banach. Canad. Math. Bull. 40 (1997), 488–97. 603Google Scholar
Maouche, A., Spectrum preserving linear mappings for scattered Jordan–Banach algebras. Proc. Amer. Math. Soc. 127 (1999), 3187–90. 603Google Scholar
Marcos, J. C., Rodríguez, A., and Velasco, M. V., A note on topological divisors of zero and division algebras. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 109 (2015), 93100.Google Scholar
Marcos, J. C. and Velasco, M. V., The Jacobson radical of a non-associative algebra and the uniqueness of the complete norm topology. Bull. London Math. Soc. 42 (2010), 1010–20.Google Scholar
Marcos, J. C. and Velasco, M. V., Continuity of homomorphisms into power-associative complete normed algebras. Forum Math. 25 (2013), 1109–25.Google Scholar
Martín, M., The group of isometries of a Banach space and duality. J. Funct. Anal. 255 (2008), 2966–76.Google Scholar
Martín, M. and Merí, J., Numerical index of some polyhedral norms on the plane. Linear Multilinear Algebra 55 (2007), 175–90.Google Scholar
Martín, M., Merí, J., and Payá, R., On the intrinsic and the spatial numerical range. J. Math. Anal. Appl. 318 (2006), 175–89.Google Scholar
Martín, M., Merí, J., and Rodríguez, A., Finite-dimensional Banach spaces with numerical index zero. Indiana Univ. Math. J. 53 (2004), 1279–89.Google Scholar
Martín, M. and Payá, R., Numerical index of vector-valued function spaces. Studia Math. 142 (2000), 269–80.Google Scholar
Martínez, J., JV-algebras. Math. Proc. Cambridge Philos. Soc. 87 (1980), 4750. 597Google Scholar
Martínez, J., Holomorphic functional calculus in Jordan–Banach algebras. In [749], pp. 125–34. 597Google Scholar
Martínez, J., Tracial elements for nonassociative H -algebras. In [733], pp. 257–68. xxv, 550Google Scholar
Martínez, J., Mena, J. F., Payá, R., and Rodríguez, A., An approach to numerical ranges without Banach algebra theory. Illinois J. Math. 29 (1985), 609–25. 673Google Scholar
Martínez, J. and Peralta, A. M., Separate weak-continuity of the triple product in dual real JB -triples. Math. Z. 234 (2000), 635–46. 243Google Scholar
Martínez, J. and Rodríguez, A., Imbedding elements whose numerical range has a vertex at zero in holomorphic semigroups. Proc. Edinburgh Math. Soc. 28 (1985), 91–5.Google Scholar
Mathieu, M., Rings of quotients of ultraprime Banach algebras, with applications to elementary operators. In [773], pp. 297–317. xxii, 408, 468, 547Google Scholar
Maurey, B., Banach spaces with few operators. In [757], pp. 1247–97.Google Scholar
Mazet, P., La preuve originale de S. Mazur pour son théorème sur les algèbres normées. Gaz. Math., Soc Math. Fr. 111 (2007), 511.Google Scholar
Mazur, S., Über konvexe Mengen in linearen normierten Räumen. Studia Math. 4 (1933), 7084.Google Scholar
Mazur, S., Sur les anneaux linéaires. C. R. Acad. Sci. Paris 207 (1938), 1025–7.Google Scholar
McCrimmon, K., Norms and noncommutative Jordan algebras. Pacific J. Math. 15 (1965), 925–56.Google Scholar
McCrimmon, K., Macdonald’s theorem with inverses. Pacific J. Math. 21 (1967), 315–25.Google Scholar
McCrimmon, K., The radical of a Jordan algebra. Proc. Nat. Acad. Sci. USA 62 (1969), 671–8. 597Google Scholar
McCrimmon, K., Noncommutative Jordan rings. Trans. Amer. Math. Soc. 158 (1971), 133. xxi, 273, 348, 411Google Scholar
McCrimmon, K. and Zel’manov, E., The structure of strongly prime quadratic Jordan algebras. Adv. Math. 69 (1988), 133222. xxi, 348, 365, 464Google Scholar
McGuigan, R., Strongly extreme points in Banach spaces. Manuscripta Math. 5 (1971), 113–22.Google Scholar
McIntosh, A., Functions and derivations of C -algebras. J. Funct. Anal. 30 (1978), 264–75.Google Scholar
Medbouhi, A. and Tajmouati, A., Calcul fonctionnel harmonique dans les algèbres de Banach alternatives involutives et applications. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), 141–52.Google Scholar
Mena, J. F. and Rodríguez, A., Weakly compact operators on non-complete normed spaces. Expo. Math. 27 (2009), 143–51.Google Scholar
Mena, J. F. and Rodríguez, A., Compact and weakly compact operators on non-complete normed spaces. In [704], pp. 205–11.Google Scholar
Meyberg, A., Identitäten und das Radikal in Jordan-Tripelsystemen. Math. Ann. 197 (1972), 203–20.Google Scholar
Milman, V. D., The infinite-dimensional geometry of the unit sphere of a Banach space. Soviet Math. Dokl. 8 (1967), 1440–4.Google Scholar
Milnor, J., Some consequences of a theorem of Bott. Ann. of Math. 68 (1958), 444–9.Google Scholar
Moore, R. T., Hermitian functionals on B-algebras and duality characterizations of C -algebras. Trans. Amer. Math. Soc. 162 (1971), 253–65.Google Scholar
Moreno, A., Distinguishing Jordan polynomials by means of a single Jordan-algebra norm. Studia Math. 122 (1997), 6773. xxii, 470Google Scholar
Moreno, A. and Rodríguez, A., On the Zel’manovian classification of prime JB -triples. J. Algebra 226 (2000), 577613. xxii, 422, 458, 460, 461Google Scholar
Moreno, A. and Rodríguez, A., On the Zel’manovian classification of prime JB - and JBW -triples. Comm. Algebra 31 (2003), 1301–28. xxii, 458, 459, 460, 461Google Scholar
Moreno, A. and Rodríguez, A., Introducing Analysis in Zel’manov’s theorems for Jordan systems. In Comptes Rendus de la Premièr Rencontre Maroco-Andalouse sur les Algèbres et leurs Applications, Tétouan, Septembre 2001, pp. 836, Université Abdelmalek Essaadi, Faculté des Sciences, Tétouan, 2003. 462Google Scholar
Moreno, A. and Rodríguez, A., A bilinear version of Holsztynski’s theorem on isometries of C(X)-spaces. Studia Math. 166 (2005), 8391.Google Scholar
Moreno, A. and Rodríguez, A., On multiplicatively closed subsets of normed algebras. J. Algebra 323 (2010), 1530–52. xxvi, 652, 653Google Scholar
Moreno, A. and Rodríguez, A., Topologically nilpotent normed algebras. J. Algebra 368 (2012), 126–68. xxvi, 652, 653, 654, 655, 656, 658Google Scholar
Moreno, G., The zero divisors of the Cayley–Dickson algebras over the real numbers. Bol. Soc. Mat. Mexicana 4 (1998), 1328.Google Scholar
Moreno, G., Alternative elements in the Cayley–Dickson algebras. In Topics in mathematical physics, general relativity and cosmology in honor of Jerzy Plebañski , pp. 333–46, World Sci. Publ., Hackensack, NJ, 2006.Google Scholar
Moutassim, A. and Rochdi, A., Sur les algèbres préhilbertiennes vérifiant ‖a 2‖ ≤‖a2 . Adv. appl. Clifford alg. 18 (2008), 269–78.Google Scholar
Nagumo, M., Einige analytishe Untersuchunger in linearen metrishen Ringen. Jap. J. Math. 13 (1936), 6180.Google Scholar
Nakamura, M., Complete continuities of linear operators. Proc. Japan Acad. 27 (1951), 544–7.Google Scholar
Navarro-Pascual, J. C. and Navarro, M. A., Unitary operators in real von Neumann algebras. J. Math. Anal. Appl. 386 (2012), 933–8.Google Scholar
Neher, E., Generators and relations for 3-graded Lie algebras, J. Algebra 155 (1993), 135. xxv, 554Google Scholar
von Neumann, J., On an algebraic generalization of the quantum mechanical formalism I. Mat. Sb. 1 (1936), 415–84.Google Scholar
Neumann, M. M., Rodríguez, A., and Velasco, M. V., Continuity of homomorphisms and derivations on algebras of vector-valued functions. Quart. J. Math. Oxford 50 (1999), 279300. 596, 709Google Scholar
Nieto, J. I., Normed right alternative algebras over the reals. Canad. J. Math. 24 (1972), 1183–6.Google Scholar
Nieto, J. I. Gateaux differentials in Banach algebras. Math. Z. 139 (1974), 2334.Google Scholar
Oja, E., On bounded approximation properties of Banach spaces. In Banach algebras 2009, pp. 219–31, Banach Center Publ. 91, Polish Acad. Sci. Inst. Math., Warsaw, 2010.Google Scholar
Okayasu, T., A structure theorem of automorphisms of von Neumann algebras. Tôhoku Math. J. 20 (1968), 199206.Google Scholar
Okubo, S., Pseudo-quaternion and pseudo-octonion algebras. Hadronic J. 1 (1978), 1250–78.Google Scholar
Okubo, S. and Osborn, J. M., Algebras with nondegenerate associative symmetric forms permitting composition. Comm. Algebra 9 (1981), 1233–61.Google Scholar
Olsen, C. L. and Pedersen, G. K., Convex combinations of unitary operators in von Neumann algebras. J. Funct. Anal. 66 (1986), 365–80.Google Scholar
Osborn, J. M., Quadratic division algebras. Trans. Amer. Math. Soc. 105 (1962), 202–21.Google Scholar
Osborn, J. M., Varieties of algebras. Adv. Math. 8 (1972), 163369.Google Scholar
Ostrowski, A., Über einige Lösungen der Funktionalgleichung Ψ(x)Ψ(y) = Ψ(xy). Acta Math. 41 (1918), 271–84.Google Scholar
Palais, R. S., The classification of real division algebras. Amer. Math. Monthly 75 (1968), 366–8.Google Scholar
Palmer, T. W., Characterizations of C -algebras. Bull. Amer. Math. Soc. 74 (1968), 538–40.Google Scholar
Palmer, T. W., Unbounded normal operators on Banach spaces. Trans. Amer. Math. Soc. 133 (1968), 385414.Google Scholar
Palmer, T. W., Characterizations of C -algebras II. Trans. Amer. Math. Soc. 148 (1970), 577–88.Google Scholar
Palmer, T. W., Real C -algebras. Pacific J. Math. 35 (1970), 195204.Google Scholar
Palmer, T. W., Spectral algebras. Rocky Mountain J. Math. 22 (1992), 293328.Google Scholar
Paterson, A. L. T., Isometries between B -algebras. Proc. Amer. Math. Soc. 22 (1969), 570–2.Google Scholar
Paterson, A. L. T. and Sinclair, A. M., Characterization of isometries between C -algebras. J. London Math. Soc. 5 (1972), 755–61.Google Scholar
Payá, R., Pérez, J., and Rodríguez, A., Non-commutative Jordan C -algebras. Manuscripta Math. 37 (1982), 87120. xx, xxi, 3, 19, 398, 411, 421Google Scholar
Payá, R., Pérez, J., and Rodríguez, A., Type I factor representations of non-commutative JB -algebras. Proc. London Math. Soc. 48 (1984), 428–44. xx, xxi, 398, 411, 421Google Scholar
Pedersen, G. K., Measure theory in C -algebras II. Math. Scand. 22 (1968), 6374.Google Scholar
Pedersen, G. K., The λ-function in operator algebras. J. Operator Theory 26 (1991), 345–81.Google Scholar
Peralta, A. M., On the axiomatic definition of real JB -triples. Math. Nachr. 256 (2003), 100–6.Google Scholar
Peralta, A. M., Positive definite hermitian mappings associated to tripotent elements. Expo. Math. 33 (2015), 252–8.Google Scholar
Peresi, L. A., Other nonassociative algebras. In The concise handbook of algebra (eds. Mikhalev, A. V. and Pilz, G. F.), pp. 343–7, Dordrecht, Kluwer Academic, 2002.Google Scholar
Pérez, J., Rico, L., and Rodríguez, A., Full subalgebras of Jordan–Banach algebras and algebra norms on JB -algebras. Proc. Amer. Math. Soc. 121 (1994), 1133–43. 336, 597Google Scholar
Pérez, J., Rico, L., Rodríguez, A., and Villena, A. R., Prime Jordan–Banach algebras with nonzero socle. Comm. Algebra 20 (1992), 1753. 598Google Scholar
Perlis, S., A characterization of the radical of an algebra. Bull. Amer. Math. Soc. 48 (1942), 128–32.Google Scholar
Phelps, R. R., Extreme points in function algebras. Duke Math. J. 32 (1965), 267–77.Google Scholar
Popa, S., On the Russo–Dye theorem. Michigan Math. J. 28 (1981), 311–15.Google Scholar
Pták, V., On the spectral radius in Banach algebras with involution. Bull. London Math. Soc. 2 (1970), 327–34.Google Scholar
Pták, V., Banach algebras with involution. Manuscripta Math. 6 (1972), 245–90.Google Scholar
Putter, P. S. and Yood, B., Banach Jordan ∗-algebras. Proc. London Math. Soc. 41 (1980), 2144. 597Google Scholar
Raeburn, I. and Sinclair, A. M., The C -algebra generated by two projections. Math. Scand. 65 (1989), 278–90.Google Scholar
Raffin, R., Anneaux a puissances commutatives and anneaux flexibles. C. R. Acad. Sci. Paris 230 (1950), 804–6.Google Scholar
Rambla, F., A counterexample to Wood’s conjecture. J. Math. Anal. Appl. 317 (2006), 659–67.Google Scholar
Ransford, T. J., A short proof of Johnson’s uniqueness-of-norm theorem. Bull. London Math. Soc. 21 (1989), 487–8.Google Scholar
Rickart, C. E., The singular elements of a Banach algebra. Duke Math. J. 14 (1947), 1063–77.Google Scholar
Rickart, C. E., The uniqueness of norm problem in Banach algebras. Ann. of Math. 51 (1950), 615–28.Google Scholar
Rickart, C. E., On spectral permanence for certain Banach algebras. Proc. Amer. Math. Soc. 4 (1953), 191–6.Google Scholar
Rickart, C. E., An elementary proof of a fundamental theorem in the theory of Banach algebras. Michigan Math. J. 5 (1958), 75–8.Google Scholar
Riesz, F., Sur certains systèmes singuliers d’équations intégrales. Ann. Sci. École Norm. Sup. 28 (1911), 3362.Google Scholar
Riesz, F., Über lineare Funktionalgleichungen. Acta Math. 41 (1916), 7198.Google Scholar
Robertson, A. G., A note on the unit ball in C -algebras. Bull. London Math. Soc. 6 (1974), 333–5.Google Scholar
Robertson, A. G. and Youngson, M. A., Positive projections with contractive complements on Jordan algebras. J. London Math. Soc. 25 (1982), 365–74. 210Google Scholar
Rochdi, A., Eight-dimensional real absolute valued algebras with left unit whose automorphism group is trivial. Int. J. Math. Math. Sci. 70 (2003), 4447–54.Google Scholar
Rochdi, A. and Rodríguez, A., Absolute valued algebras with involution. Comm. Algebra 37 (2009), 1151–9.Google Scholar
Rodríguez, A., Algebras estelares de Banach con elemento unidad. In Actas de las I Jornadas Matemáticas Hispano-Lusitanas, pp. 189210, Madrid, 1973.Google Scholar
Rodríguez, A., Derivaciones en álgebras normadas y commutatividad. Cuadernos del Dpto. de Estadística Matemática (Granada) 2 (1975), 5168.Google Scholar
Rodríguez, A., Teorema de estructura de los Jordan-isomorfismos de las C -álgebras. Rev. Mat. Hispano-Americana 37 (1977), 114–28.Google Scholar
Rodríguez, A., Rango numérico y derivaciones cerradas de las álgebras de Banach. In V Jornadas luso-espanholas de matemáticas, pp. 179200, Aveiro, 1978.Google Scholar
Rodríguez, A., A Vidav–Palmer theorem for Jordan C -algebras and related topics. J. London Math. Soc. 22 (1980), 318–32.Google Scholar
Rodríguez, A., Non-associative normed algebras spanned by hermitian elements. Proc. London Math. Soc. 47 (1983), 258–74. 210Google Scholar
Rodríguez, A., The uniqueness of the complete algebra norm topology in complete normed nonassociative algebras. J. Funct. Anal. 60 (1985), 115. 548, 597Google Scholar
Rodríguez, A., Mutations of C -algebras and quasiassociative JB -algebras. Collectanea Math. 38 (1987), 131–5.Google Scholar
Rodríguez, A., Jordan axioms for C -algebras. Manuscripta Math. 61 (1988), 279314. xxiv, 474, 549Google Scholar
Rodríguez, A., Automatic continuity with application to C -algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 345–7.Google Scholar
Rodríguez, A., An approach to Jordan–Banach algebras from the theory of nonassociative complete normed algebras. In [749], pp. 1–57. 584, 585, 586Google Scholar
Rodríguez, A., One-sided division absolute valued algebras. Publ. Mat. 36 (1992), 925–54.Google Scholar
Rodríguez, A., Closed derivations of Banach algebras. In Homenaje a Pablo Bobillo Guerrero, pp. 21–8, Univ. Granada, Granada, 1992.Google Scholar
Rodríguez, A., Primitive nonassociative normed algebras and extended centroid. In [734], pp. 233–43. 408, 601, 602Google Scholar
Rodríguez, A., Absolute valued algebras of degree two. In [733], pp. 350–6.Google Scholar
Rodríguez, A., Jordan structures in Analysis. In [764], pp. 97–186. xxii, 338, 340, 408, 462, 467, 549, 550, 553, 597, 601Google Scholar
Rodríguez, A., Continuity of densely valued homomorphisms into H -algebras. Quart . J. Math. Oxford 46 (1995), 107–18. xxiv, 546, 548, 549Google Scholar
Rodríguez, A., Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces. In Encuentro de Análisis Matemático, Homenaje al profesor B. Rodríguez-Salinas (eds. Bombal, F., Hernández, F. L., Jiménez y, P. de María, J. L.), Rev. Mat. Univ. Complutense Madrid 9 (1996), 149–89.Google Scholar
Rodríguez, A., Isometries and Jordan isomorphisms onto C -algebras. J. Operator Theory 40 (1998), 7185. 274, 346Google Scholar
Rodríguez, A., Continuity of homomorphisms into normed algebras without topological divisors of zero. Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.) 94 (2000), 505–14. xxv, 595Google Scholar
Rodríguez, A., Sobre el tamaño de los conjuntos de números. In Actas del Encuentro de Matemáticos Andaluces, Sevilla 2000, Volumen I, pp. 235–48, Secretariado de Publicaciones de la Universidad de Sevilla, Sevilla, 2001.Google Scholar
Rodríguez, A., A numerical range characterization of uniformly smooth Banach spaces. Proc. Amer. Math. Soc. 129 (2001), 815–21.Google Scholar
Rodríguez, A., Banach–Jordan algebra. In [741], pp. 55–7. 462Google Scholar
Rodríguez, A., Absolute-valued algebras, and absolute-valuable Banach spaces. In Advanced Courses of Mathematical Analysis I, Proceedings of the First International School Cádiz, Spain 22–27 September 2002 (eds. Aizpuru-Tomás, A. and León-Saavedra, F.), pp. 99155, World Scientific, 2004.Google Scholar
Rodríguez, A., Numerical ranges of uniformly continuous functions on the unit sphere of a Banach space. J. Math. Anal. Appl. 297 (2004), 472–6. 208Google Scholar
Rodríguez, A., On Urbanik’s axioms for absolute valued algebras with involution. Comm. Algebra 36 (2008), 2588–92.Google Scholar
Rodríguez, A., Banach space characterizations of unitaries: a survey. J. Math. Anal. Appl. 369 (2010), 168–78.Google Scholar
Rodríguez, A., Approximately norm-unital products on C -algebras, and a nonassociative Gelfand–Naimark theorem. J. Algebra 347 (2011), 224–46. 421Google Scholar
Rodríguez, A., Slinko, A. M., and Zel’manov, E. I., Extending the norm from Jordan– Banach algebras of hermitian elements to their associative envelopes. Comm. Algebra 22 (1994), 1435–55. xxii, xxiii, 437, 470, 471, 472Google Scholar
Rodríguez, A. and Velasco, M. V., Continuity of homomorphisms and derivations on Banach algebras with an involution. In Function Spaces; Proceedings of the Third Conference on Function Spaces, May 19–23, 1998, Southern Illinois University at Edwardsville (ed. Jarosz, K.), pp. 289–98, Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999. xxii, 474, 475Google Scholar
Rodríguez, A. and Velasco, M. V., A non-associative Rickart’s dense-range-homomorphism theorem. Quart. J. Math. Oxford 54 (2003), 367–76. 597Google Scholar
Rordam, M., Advances in the theory of unitary rank and regular approximation. Ann. of Math. 128 (1988), 153–72.Google Scholar
Rosenthal, H., The Lie algebra of a Banach space. In Banach Spaces, pp. 129–57, Lecture Notes in Math. 1166, 1985.Google Scholar
Rosenthal, H., Functional Hilbertian sums. Pacific J. Math. 124 (1986), 417–67.Google Scholar
Rota, G.-C. and Strang, W. G., A note on the joint spectral radius. Indag. Math. 22 (1960), 379–81. xxvi, 650Google Scholar
Rowen, L. H., A short proof of the Chevalley–Jacobson density theorem, and a generalization. Amer. Math. Monthly 85 (1978), 185–6.Google Scholar
Ruan, Z.-J., Subspaces of C*-algebras. J. Funct. Anal. 76 (1988), 217–30.Google Scholar
Russo, B., Structure of JB -triples. In [764], pp. 209–80.Google Scholar
Russo, B. and Dye, H. A., A note on unitary operators in C -algebras. Duke Math. J. 33 (1966), 413–16.Google Scholar
Sakai, S., On a conjecture of Kaplansky. Tôhoku Math. J. 12 (1960), 31–3.Google Scholar
Sasiada, E. and Cohn, P. M., An example of a simple radical ring. J. Algebra 5 (1967), 373–7. 659Google Scholar
Schafer, R. D., On the algebras formed by the Cayley–Dickson process. Amer. J. Math. 76 (1954), 435–46.Google Scholar
Schafer, R. D., Noncommutative Jordan algebras of characteristic 0. Proc. Amer. Math. Soc. 6 (1955), 472–5.Google Scholar
Schafer, R. D., Generalized standard algebras. J. Algebra 12 (1969), 386417. 657Google Scholar
Schatz, J. A., Review of [273]. Math. Rev. 14 (1953), 884.Google Scholar
Schauder, J., Über lineare, vollstetige Funktionaloperationen. Studia Math. 2 (1930), 183–96.Google Scholar
Schoenberg, I. J., A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal. Proc. Amer. Math. Soc. 3 (1952), 961–4.Google Scholar
Schue, J. R., Hilbert space methods in the theory of Lie algebras, Trans. Amer. Math. Soc. 95 (1960), 6980. 553, 554Google Scholar
Schue, J. R., Cartan decompositions for L -algebras. Trans. Amer. Math. Soc. 98 (1961), 334–49. 553Google Scholar
Schur, 1. I., Neue Begründung der Theorie der Gruppencharaktere. Sitzungsberichte der Preuβischen Akademie der Wissenschaften 1905 Physik-Math. Klasse 406–32. Reprinted in Gesammelte Abhandlungen Vol. I pp. 143–69, Spriger, Berlin, 1973.Google Scholar
Segal, I. E., Irreducible representations of operator algebras. Bull. Amer. Math. Soc. 53 (1947), 7388.Google Scholar
Segre, B., La teoria delle algebre ed alcune questione di realtà. Univ. Roma, Ist. Naz. Alta. Mat., Rend. Mat. e Appl., serie 5 13 (1954), 157–88.Google Scholar
Shelah, S. and Steprans, J., A Banach space on which there are few operators. Proc. Amer. Math. Soc. 104 (1988), 101–5.Google Scholar
Sherman, D., A new proof of the noncommutative Banach–Stone theorem. Quantum probability , 363–75, Banach Center Publ. 73, Polish Acad. Sci. Inst. Math., Warsaw, 2006.Google Scholar
Shilov, G., On the extension of maximal ideals. C. R. (Doklady) Acad. Sci. URSS 29 (1940), 83–4.Google Scholar
Shirali, S. and Ford, J. W. M., Symmetry in complex involutory Banach algebras. II. Duke Math. J. 37 (1970), 275–80.Google Scholar
Shirokov, F. V., Proof of a conjecture by Kaplansky. (In Russian.) Uspekhi Mat. Nauk 11 (1956) 167–8.Google Scholar
Shirshov, A. I., On special J-rings. (In Russian.) Mat. Sb. 38 (80) (1956), 149–66.Google Scholar
Shirshov, A. I., On some non-associative nil-rings and algebraic algebras. Mat. Sb. 41 (83) (1957), 381–94.Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Joint spectral radius, operator semigroups, and a problem of W. Wojtynski. J. Funct. Anal. 177 (2000), 383441. xxvi, 652, 653, 654, 656Google Scholar
Shultz, F. W., On normed Jordan algebras which are Banach dual spaces. J. Funct. Anal. 31 (1979), 360–76. 19, 398, 401Google Scholar
Siddiqui, A. A., Self-adjointness in unitary isotopes of JB -algebras. Arch. Math. 87 (2006), 350–8.Google Scholar
Siddiqui, A. A., Asymmetric decompositions of vectors in JB -algebras. Arch. Math. (Brno) 42 (2006), 159–66.Google Scholar
Siddiqui, A. A., JB -algebras of topological stable rank 1. Int. J. Math. Math. Sci. 2007, Art. ID 37186, 24 pp.Google Scholar
Siddiqui, A. A., A proof of the Russo–Dye theorem for JB -algebras. New York J. Math. 16 (2010), 5360.Google Scholar
Siddiqui, A. A., Convex combinations of unitaries in JB -algebras. New York J. Math. 17 (2011), 127–37.Google Scholar
Siddiqui, A. A., The λ u -function in JB -algebras. New York J. Math. 17 (2011), 139–47.Google Scholar
Sinclair, A. M., Jordan automorphisms on a semisimple Banach algebra. Proc. Amer. Math. Soc. 25 (1970), 526–8.Google Scholar
Sinclair, A. M., Jordan homomorphisms and derivations on semisimple Banach algebras. Proc. Amer. Math. Soc. 24 (1970), 209–14.Google Scholar
Sinclair, A. M., The states of a Banach algebra generate the dual. Proc. Edinburgh Math. Soc. 17 (1970/71), 341–4.Google Scholar
Sinclair, A. M., The norm of a hermitian element in a Banach algebra. Proc. Amer. Math. Soc. 28 (1971), 446–50.Google Scholar
Sinclair, A. M., The Banach algebra generated by a derivation. In Spectral theory of linear operators and related topics (Timisoara/Herculane, 1983), pp. 241–50, Oper. Theory Adv. Appl. 14, Birkhäuser, Basel, 1984.Google Scholar
Singer, I. M. and Wermer, J., Derivations on commutative normed algebras. Math. Ann. 129 (1955), 260–4.Google Scholar
Skorik, A. and Zaidenberg, M., On isometric reflexions in Banach spaces. Math. Physics, Analysis, Geometry 4 (1997), 212–47.Google Scholar
Skosyrskii, V. G., Strongly prime noncommutative Jordan algebras. (In Russian.) Trudy Inst. Mat. (Novosibirk) 16 (1989), 131–64, Issled. po Teor. Kolets i Algebr, 198–9. 411, 422Google Scholar
Skosyrskii, V. G., Primitive Jordan algebras. Algebra Logic 31 (1993), 110–20. xxii, 462Google Scholar
Slinko, A. M., Complete metric Jordan algebras. Mat. Zametki 447 (1990), 100–5. English translation: Math. Notes 47 (1990), 491–4. 597Google Scholar
Slinko, A. M., 1, 2, 4, 8, … What comes next? Extracta Math. 19 (2004), 155–61.Google Scholar
Smiley, M. F., The radical of an alternative ring. Ann. of Math. 49 (1948), 702–9.Google Scholar
Smiley, M. F., Right H -algebras. Proc. Amer. Math. Soc. 4 (1953), 14.Google Scholar
Smiley, M. F., Real Hilbert algebras with identity. Proc. Amer. Math. Soc. 16 (1965) 440–1.Google Scholar
Smith, R. R., On Banach algebra elements of thin numerical range. Math. Proc. Cambridge Philos. Soc. 86 (1979), 7183.Google Scholar
Smith, R. R., The numerical range in the second dual of a Banach algebra. Math. Proc. Cambridge Philos. Soc. 89 (1981), 301–7.Google Scholar
Šmulyan, V., Sur la structure de la sphère unitaire dans l’espace de Banach. Math. Sb. 9 (1941), 545–61.Google Scholar
Spatz, I. N., Smooth Banach algebras. Proc. Amer. Math. Soc. 22 (1969), 328–9.Google Scholar
Spitkovsky, I., Once more on algebras generated by two projections. Linear Algebra Appl. 208 / 209 (1994), 377–95.Google Scholar
Spurný, J., A note on compact operators on normed linear spaces. Expo. Math. 25 (2007), 261–3.Google Scholar
Stachó, L. L., A projection principle concerning biholomorphic automorphisms. Acta Sci. Math. (Szeged) 44 (1982), 99124. xix, 207, 210Google Scholar
Steen, S. W. P., Introduction to the theory of operators. V. Metric rings, Proc. Cambridge Philos. Soc. 36 (1940), 139–49. 550Google Scholar
Stinespring, W. F., Positive functions on C -algebras. Proc. Amer. Math. Soc. 6, (1955), 211–16.Google Scholar
Stone, M. H., Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41 (1937), 375481.Google Scholar
Størmer, E., On the Jordan structure of C -algebras. Trans. Amer. Math. Soc. 120 (1965), 438–47.Google Scholar
Størmer, E., Jordan algebras of type I. Acta Math. 115 (1966), 165–84. 339Google Scholar
Størmer, E., Irreducible Jordan algebras of self-adjoint operators. Trans. Amer. Math. Soc. 130 (1968), 153–66. 339Google Scholar
Strasek, R. and Zalar, B., Uniform primeness of classical Banach Lie algebras of compact operators. Publ. Math. Debrecen 61 (2002), 325–40.Google Scholar
Strzelecki, E., Metric properties of normed algebras. Studia Math. 23 (1963), 4151.Google Scholar
Strzelecki, E., Power-associative regular real normed algebras. J. Austral. Math. Soc. 6 (1966), 193209.Google Scholar
Suttles, D., A counterexample to a conjecture of Albert. Notices Amer. Math. Soc., 19 (1972), A-566.Google Scholar
Szankowski, A., B(H) does not have the approximation property. Acta Math. 147 (1981), 89108.Google Scholar
Talponen, J., A note on the class of superreflexive almost transitive Banach spaces. Extracta Math. 23 (2008), 16.Google Scholar
Terekhin, P. A., Trigonometric algebras. J. Math. Sci. (New York) 95 (1999), 2156–60.Google Scholar
Thomas, M. P., The image of a derivation is contained in the radical. Ann. of Math. 128 (1988), 435–60.Google Scholar
Thomas, M. P., Primitive ideals and derivations on noncommutative Banach algebras. Pacific J. Math. 159 (1993), 139–52.Google Scholar
Toeplitz, O., Das algebraische Analogon zu einem Satze von Fejer. Math. Z. 2 (1918), 187–97.Google Scholar
Topping, D. M., An isomorphism invariant for spin factors. J. Math. Mech. 15 (1966), 1055–63.Google Scholar
Turovskii, Yu. V., On spectral properties of Lie subalgebras and on the spectral radius of subsets of a Banach algebra. (In Russian.) Spectral theory of operators and its applications, 6 (1985), 144–81. xxvi, 651Google Scholar
Uchiyama, M., Operator monotone functions which are defined implicitly and operator inequalities. J. Funct. Anal. 175 (2000), 330–47.Google Scholar
Urbanik, K., Absolute valued algebras with an involution. Fundamenta Math. 49 (1961), 247–58.Google Scholar
Urbanik, K., Remarks on ordered absolute valued algebras. Colloq. Math. 11 (1963), 31–9.Google Scholar
Urbanik, K. and Wright, F. B., Absolute valued algebras. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 285–6.Google Scholar
Urbanik, K. and Wright, F. B., Absolute valued algebras. Proc. Amer. Math. Soc. 11 (1960), 861–6.Google Scholar
Velasco, M. V., Spectral theory for non-associative complete normed algebras and automatic continuity. J. Math. Anal. Appl. 351 (2009), 97106.Google Scholar
Vesentini, E., On the subharmonicity of the spectral radius. Boll. Un. Mat. Ital. 1 (1968), 427–9.Google Scholar
Vidav, I., Eine metrische Kennzeichnung der selbstadjungierten Operatoren. Math. Z. 66 (1956), 121–8.Google Scholar
Villena, A. R., Continuity of derivations on H -algebras. Proc. Amer. Math. Soc. 122 (1994), 821–6. xxiv, 548, 549Google Scholar
Villena, A. R., Derivations on Jordan–Banach algebras. Studia Math. 118 (1996), 205–29. 466, 548Google Scholar
Villena, A. R., Automatic continuity in associative and nonassociative context. Irish Math. Soc. Bulletin 46 (2001), 4376.Google Scholar
Villena, A. R., Epimorphisms onto derivation algebras. Proc. Edinburgh Math. Soc. 46 (2003), 379–82.Google Scholar
Viola Devapakkiam, C., Jordan algebras with continuous inverse. Math. Japon. 16 (1971), 115–25. 597Google Scholar
Vowden, B. J., On the Gelfand–Neumark theorem. J. London Math. Soc. 42 (1967), 725–31.Google Scholar
Walsh, B., Classroom notes: The scarcity of cross products on Euclidean spaces. Amer. Math. Monthly 74 (1967), 188–94.Google Scholar
Wark, H. M., A non-separable reflexive Banach space on which there are few operators. J. London Math. Soc. 64 (2001), 675–89.Google Scholar
Wichmann, J., Hermitian ∗-algebras which are not symmetric. J. London Math. Soc. 8 (1974), 109–12.Google Scholar
Wichmann, J., On commutative B -equivalent algebras. Notices Amer. Math. Soc. (1975), Abstract 720–46–19.Google Scholar
Wichmann, J., The symmetric radical of an algebra with involution. Arch. Math. (Basel) 30 (1978), 83–8.Google Scholar
Wilansky, A., Letter to the Editor. Amer. Math. Monthly 91 (1984), 531.Google Scholar
Wilkins, T. J. D., Inessential ideals in Jordan–Banach algebras. Bull. London Math. Soc. 29 (1997), 7381. 603Google Scholar
Wojtaszczyk, P., Some remarks on the Daugavet equation. Proc. Amer. Math. Soc. 115 (1992), 1047–52.Google Scholar
Wood, G. V., Maximal symmetry in Banach spaces. Proc. Royal Irish Acad. 82A (1982), 177–86.Google Scholar
Wood, G. V., Maximal algebra norms. In Trends in Banach spaces and operator theory (Memphis, TN, 2001), pp. 335–45, Contemp. Math. 321, Amer. Math. Soc., Providence, RI, 2003.Google Scholar
Wright, F. B., Absolute valued algebras. Proc. Nat. Acad. Sci. USA 39 (1953), 330–2.Google Scholar
Wright, J. D. M., Jordan C -algebras. Michigan Math. J. 24 (1977), 291302. xx, 347, 398, 401Google Scholar
Wright, J. D. M. and Youngson, M. A., A Russo Dye theorem for Jordan C -algebras. In Functional analysis: surveys and recent results (Proc. Conf., Paderborn, 1976) (eds. Bierstedt, K. D. and Fuchssteiner, F.), pp. 279–82, North-Holland Math. Stud. 27, North-Holland, Amsterdam, 1977.Google Scholar
Wright, J. D. M. and Youngson, M. A., On isometries of Jordan algebras. J. London Math. Soc. 17 (1978), 339–44.Google Scholar
Wu, W., Locally pre-C -equivalent algebras. Proc. Amer. Math. Soc. 131 (2003), 555–62.Google Scholar
Yood, B., Topological properties of homomorphisms between Banach algebras. Amer. J. Math. 76 (1954), 155–67.Google Scholar
Yood, B., Homomorphisms on normed algebras. Pacific J. Math. 8 (1958), 373–81.Google Scholar
Yood, B., Faithful ∗-representations of normed algebras. Pacific J. Math. 10 (1960), 345–63.Google Scholar
Yood, B., Ideals in topological rings. Canad. J. Math. 16 (1964), 2845.Google Scholar
Yood, B., On axioms for B -algebras. Bull. Amer. Math. Soc. 76 (1970), 80–2.Google Scholar
Yost, D., A base norm space whose cone is not 1-generating. Glasgow Math. J. 25 (1984), 35–6. 690Google Scholar
Yost, D., Review of [650]. Zbl. Mat. 0544.46014.Google Scholar
Youngson, M. A., A Vidav theorem for Banach Jordan algebras. Math. Proc. Cambridge Philos. Soc. 84 (1978), 263–72.Google Scholar
Youngson, M. A., Equivalent norms on Banach Jordan algebras. Math. Proc. Cambridge Philos. Soc. 86 (1979), 261–9. 597Google Scholar
Youngson, M. A., Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. 22 (1979), 93104.Google Scholar
Youngson, M. A., Nonunital Banach Jordan algebras and C -triple systems. Proc. Edinburgh Math. Soc. 24 (1981), 1929. 210Google Scholar
Zalar, B., Inner product characterizations of classical Cayley–Dickson algebras. In [733], pp. 405–9.Google Scholar
Zalar, B., On Hilbert spaces with unital multiplication. Proc. Amer. Math. Soc. 123 (1995), 1497–501.Google Scholar
Zalduendo, I., A simple example of a noncommutative Arens product. Publ. Mat. 35 (1991), 475–7.Google Scholar
Zelazko, W., On generalized topological divisors of zero in real m-convex algebras. Studia Math. 28 (1966/1967), 241–4.Google Scholar
Zeller-Meier, G., Sur les automorphismes des algèbres de Banach. C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A1131–2.Google Scholar
Zel’manov, E. I., Absolute zero-divisors and algebraic Jordan algebras. Siberian Math. J. 23 (1982), 841–54. 600Google Scholar
Zel’manov, E. I., On prime Jordan algebras II. Siberian Math. J. 24 (1983), 89104. xxi, 348, 364, 365, 366, 367, 401, 437Google Scholar
Zel’manov, E. I., On prime Jordan triple systems III. Siberian Math. J. 26 (1985), 7182. xxii, 421, 437, 438, 459, 461Google Scholar
Zemánek, J., A note on the radical of a Banach algebra. Manuscripta Math. 20 (1977), 191–6.Google Scholar
Zettl, H., A characterization of ternary rings of operators. Adv. Math. 48 (1983), 117–43. 459Google Scholar
Zhevlakov, K. A., Solvability of alternative nil-rings. Sibirsk. Mat. Z. 3 (1962), 368–77.Google Scholar
Zhevlakov, K. A., Coincidence of Smiley and Kleinfeld radicals in alternative rings. Algebra Logic 8 (1969), 175–81.Google Scholar
Zorn, M., Theorie der alternativen Ringe. Abh. Math. Sem. Univ. Hamburg 8 (1930), 123–47.Google Scholar
Zorn, M., Alternativkörper und quadratische Systeme. Abh. Math. Sem. Univ. Hamburg 9 (1933), 395402.Google Scholar
Albert, A. A., Structure of algebras. Revised printing, Amer. Math. Soc. Colloq. Publ. 24, American Mathematical Society, Providence, RI, 1961.Google Scholar
Albiac, F. and Kalton, N. J., Topics in Banach space theory . Grad. Texts in Math. 233, Springer, New York, 2006. 213, 236Google Scholar
Alfsen, E. M. and Shultz, F. W., Non-commutative spectral theory for affine function spaces on convex sets . Mem. Amer. Math. Soc. 6 (1976), no. 172.Google Scholar
Alfsen, E. M. and Shultz, F. W., Geometry of state spaces of operator algebras. Mathematics: Theory and Applications. Birkhäuser Boston, Inc., Boston, MA, 2003. 331, 411Google Scholar
Aliprantis, C. D. and Border, K. C., Infinite dimensional analysis. A hitchhiker’s guide. Third edition. Springer, Berlin, 2006.Google Scholar
Allan, G. R., Introduction to Banach spaces and algebras. Prepared for publication and with a preface by H. Garth Dales. Oxf. Grad. Texts Math. 20, Oxford University Press, Oxford, 2011.Google Scholar
Amir, D., Characterizations of inner product spaces. Oper. Theory Adv. Appl. 20, Birkhäuser Verlag, Basel–Boston–Stuttgart, 1986.Google Scholar
Andrunakievich, V. A. and Rjabuhin, Yu. M., Radicals of algebras and structural theory. (In Russian.) Contemporary Algebra ‘Nauka’, Moscow, 1979. 633 Google Scholar
Ara, P. and Mathieu, M., Local multipliers of C-algebras. Springer Monogr. Math., Springer, London, 2003. 401, 408, 550Google Scholar
Argyros, S. A. and Tolias, A., Methods in the theory of hereditarily indecomposable Banach spaces . Mem. Amer. Math. Soc. 170 (2004), no. 806.Google Scholar
Ash, R. B. and Novinger, W. P., Complex variables. Dover Publications, 2007.Google Scholar
Asimow, L. and Ellis, A. J., Convexity theory and its applications in functional analysis. London Math. Soc. Monogr. 16, Academic Press, London, 1980.Google Scholar
Aupetit, B., Propriétés spectrales des algèbres de Banach. Lecture Notes in Math. 735, Springer, Berlin, 1979. 401, 436, 498, 596, 597Google Scholar
Aupetit, B., A primer on spectral theory. Universitext, Springer, New York, 1991. 597, 599Google Scholar
Ayupov, S., Rakhimov, A., and Usmanov, S., Jordan, real and Lie structures in operator algebras . Math. Appl. 418, Kluwer Academic Publishers Group, Dordrecht, 1997.Google Scholar
Banach, S., Theory of linear operations. Translated from the French by F. Jellett. With comments by A. Pełczyński and Cz. Bessaga. North-Holland Math. Library 38, North-Holland Publishing Co., Amsterdam, 1987.Google Scholar
Beidar, K. I., Martindale, W. S. III, and Mikhalev, A. V., Rings with generalized identities . Monographs Textbooks Pure Appl. Math. 196, Marcel Dekker, New York, 1996. 401, 602Google Scholar
Beltita, D., Smooth homogeneous structures in operator theory. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 137, Chapman & Hall/CRC, Boca Raton, FL, 2006. xxiv, xxv, 154, 155, 174, 549, 554Google Scholar
Beltita, D. and Sabac, M., Lie algebras of bounded operators . Oper. Theory Adv. Appl. 120, Birkhäuser Verlag, Basel, 2001.Google Scholar
Berberian, S. K., Lectures in functional analysis and operator theory. Grad. Texts in Math. 15, Springer, New York–Heidelberg, 1974. 157, 183, 539Google Scholar
Blecher, D. P. and Merdy, Ch. Le, Operator algebras and their modules – an operator space approach. London Math. Soc. Monogr. New Series 30, Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford, 2004.Google Scholar
Block, R. E., Jacobson, N., Osborn, J. M., Saltman, D. J., and Zelinsky, D. (eds.), Adrian Albert, A., Collected mathematical papers: Associative algebras and Riemann matrices, Part 1. Amer. Math. Soc., Providence, RI, 1993. 664, 678Google Scholar
Block, R. E., Jacobson, N., Osborn, J. M., Saltman, D. J., and Zelinsky, D. (eds.), Adrian Albert, A., Collected mathematical papers: Nonassociative algebras and miscellany, Part 2. Amer. Math. Soc., Providence, RI, 1993. 664, 699Google Scholar
Boas, R. P., Entire functions. Academic Press Inc., New York, 1954.Google Scholar
Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras. London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, Cambridge, 1971.Google Scholar
Bonsall, F. F. and Duncan, J., Numerical ranges II. London Math. Soc. Lecture Note Ser. 10, Cambridge University Press, Cambridge, 1973.Google Scholar
Bonsall, F. F. and Duncan, J., Complete normed algebras. Ergeb. Math. Grenzgeb. 80, Springer, Berlin, 1973. xvii, 436, 545, 551, 584, 659Google Scholar
Bourbaki, N., Éléments de mathématique. Fasc. XXXII. Théories spectrales. Chapitre I: Algèbres normées. Chapitre II: Groupes localement compacts commutatifs . Actualités Scientifiques et Industrielles 1332, Hermann, Paris, 1967.Google Scholar
Bratteli, O., Derivations, dissipations and group actions on C-algebras . Lecture Notes in Math. 1229, Springer, Berlin, 1986.Google Scholar
Bratteli, O. and Robinson, D. W., Operator algebras and quantum statistical mechanics II . Texts Monographs Phys., Springer, New York, 1981.Google Scholar
Braun, H. and Koecher, M., Jordan-Algebren. Grundlehren Math. Wiss. 128, Springer, Berlin–New York, 1966.Google Scholar
Brelot, M., On topologies and boundaries in potential theory. (Enlarged edition of a course of lectures delivered in 1966). Lecture Notes in Math. 175, Springer, Berlin–New York, 1971.Google Scholar
Brešar, M., Chebotar, M. A., and Martindale, W. S. III, Functional identities. Front. Math., Birkhäuser Verlag, Basel, 2007. 602 Google Scholar
Caradus, S. R., Pfaffenberger, W. E., and Yood, B., Calkin algebras and algebras of operators on Banach spaces. Lecture Notes in Pure and Appl. Math. 9, Marcel Dekker Inc., New York, 1974.Google Scholar
Carmona, J., Morales, A., Peralta, A. M., and Ramírez, M. I. (eds.), Proceedings of Jordan structures in algebra and analysis meeting. Tribute to El Amin Kaidi for his 60th birthday. Almería 2009. Editorial Círculo Rojo, Almería 2010. 669, 674, 682Google Scholar
Castellón, A., Cuenca, J. A., Fernández, A., and Martín, C. (eds.), Proceedings of the International Conference on Jordan Structures (Málaga, 1997). Univ. Málaga, Málaga, 1999. 679, 680, 700, 707Google Scholar
Cerdà, J., Linear functional analysis. Grad. Stud. Math. 116, American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, 2010.Google Scholar
Chae, S. B., Holomorphy and calculus in normed spaces. With an appendix by Angus E. Taylor. Monographs Textbooks Pure Appl. Math. 92. Marcel Dekker Inc., New York, 1985. 23, 53Google Scholar
Chandid, A., Algèbres absolument valuées qui satisfont à (x p , x q , x r ) = 0. PhD thesis, Casablanca 2009.Google Scholar
Choquet, G., Cours d’analyse. Tome II: Topologie. Masson et Cie, Editeurs, Paris, 1964.Google Scholar
Chu, C.-H., Jordan structures in geometry and analysis. Cambridge Tracts in Math. 190, Cambridge University Press, New York, 2012. xix, 174, 207, 209, 210, 597, 711Google Scholar
Conway, J. B., A course in functional analysis. Second edition. Grad. Texts in Math. 96, Springer, New York, 1990.Google Scholar
Conway, J. H. and Smith, D. A., On quaternions and octonions: their geometry, arithmetic, and symmetry. A K Peters, Ltd., Natick, MA, 2003.Google Scholar
Cowie, E. R., Isometries in Banach algebras. PhD thesis, Swansea 1981.Google Scholar
Cuenca, J. A., Sobre H∗-álgebras no asociativas. Teoría de estructura de las H∗-álgebras de Jordan no conmutativas semisimples . PhD thesis, Granada 1982, Secretariado de Publicaciones de la Universidad de Málaga, 1984. xxiii, 545, 548, 597Google Scholar
Dales, H. G., Banach algebras and automatic continuity. London Math. Soc. Monogr. New Series 24, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 2000. 267, 414Google Scholar
Day, M. M., Normed linear spaces. Ergeb. Math. Grenzgeb. 21, Springer, Berlin, 1973.Google Scholar
Defant, A. and Floret, K., Tensor norms and operator ideals. North-Holland Math. Stud. 176, North-Holland Publishing Co., Amsterdam, 1993. 267, 356, 416, 646Google Scholar
Diestel, J., Geometry of Banach spaces – Selected topics, Lecture Notes in Math. 485, Springer, Berlin–Heidelberg–New York, 1975.Google Scholar
Diestel, J., Fourie, J. H., and Swart, J., The metric theory of tensor products . Grothendieck’s résumé revisited. American Mathematical Society, Providence, RI, 2008.Google Scholar
Diestel, J. and Uhl, J. J. Jr., Vector measures . Mathematical Surveys 15, American Mathematical Society, Providence, RI, 1977.Google Scholar
Dineen, S., The Schwarz lemma. Oxford Math. Monogr., Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1989. 79, 87, 88, 207, 211Google Scholar
Deville, R., Godefroy, G., and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs Surveys Pure Appl. Math. 64, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993.Google Scholar
Dixmier, J., Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann). Deuxième édition, revue et augmentée. Cahiers Scientifiques 25, Gauthier-Villars Éditeur, Paris, 1969. 492, 506Google Scholar
Dixmier, J., Les C∗-algèbres et leurs représentations. Deuxième édition. Cahiers Scientifiques 29, Gauthier-Villars Éditeur, Paris, 1969.Google Scholar
Doran, R. S. and Belfi, V. A., Characterizations of C∗-algebras: The Gelfand– Naimark theorems. Monographs Textbooks Pure Appl. Math. 101, Marcel Dekker, New York–Basel, 1986. xvii, 401Google Scholar
Dunford, N. and Schwartz, J. T., Linear operators. Part I. General theory. With the assistance of W. G. Bade and R. G. Bartle. Reprint of the 1958 original. Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1988. 12, 533, 541Google Scholar
Ebbinghaus, H.-D., Hermes, H., Hirzbruch, F., Koecher, H., Mainzer, K., Neukirch, J., Prestel, A., and Remmert, R., Numbers . Grad. Texts in Math. 123, Springer, New York, 1991. 409 Google Scholar
Elduque, A. and Myung, H. Ch., Mutations of alternative algebras . Math. Appl. 278, Kluwer Academic Publishers Group, Dordrecht, 1994.Google Scholar
Fabian, M., Habala, P., Hájek, P., Montesinos, V., and Zizler, V., Banach space theory. The basis for linear and nonlinear analysis . CMS Books Math., Springer, New York, 2011. 247, 249, 288, 338Google Scholar
Fleming, R. J. and Jamison, J. E., Isometries on Banach spaces. Vol. 1. Function spaces. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 129, Chapman & Hall/CRC, Boca Raton, FL, 2003.Google Scholar
Fleming, R. J. and Jamison, J. E., Isometries on Banach spaces. Vol. 2. Vector-valued function spaces. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 138, Chapman & Hall/CRC, Boca Raton, FL, 2008.Google Scholar
Friedmann, Y. and Scarr, T., Physical applications of homogeneous balls. Prog. Math. Phys. 40, Birhäuser, Boston, 2005. 207 Google Scholar
González, S. (ed.), Nonassociative algebra and its applications (Oviedo, 1993). Math. Appl. 303, Kluwer Academic Publishers, Dordrecht–Boston–London 1994. 679, 681, 685, 690, 702, 706Google Scholar
González, S. and Myung, H. Ch. (eds.), Nonassociative algebraic models. Proceedings of the workshop held at the Universidad de Zaragoza, Zaragoza, April 1989 . Nova Science Publishers, Inc., Commack, NY, 1992. 671, 675, 685, 701, 702, 709Google Scholar
Goodearl, K. R., Notes on real and complex C-algebras. Shiva Mathematics Series 5. Shiva Publishing Ltd., Nantwich, 1982.Google Scholar
Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. (1955), no. 16.Google Scholar
Hamilton, W. R., On quaternions, or on a new system of imaginaries in Algebra. Philosophical Magazine, (1844–1850), ed. D. R. Wilkins, 2000. http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/OnQuat/OnQuat.pdf Google Scholar
Hanche-Olsen, H. and Størmer, E., Jordan operator algebras . Monographs and Studies in Mathematics 21, Pitman, Boston, 1984. xviii, xx, xxi, 3, 8, 9, 11, 12, 13, 14, 286, 330, 332, 339, 347, 348, 362, 398, 399, 401, 416, 551Google Scholar
Harmand, P., Werner, D., and Werner, W., M-ideals in Banach spaces and Banach algebras. Lecture Notes in Math. 1547, Springer, Berlin, 1993. 19, 266, 267Google Scholar
de la Harpe, P., Classical Banach–Lie algebras and Banach–Lie groups of operators in Hilbert space. Lecture Notes in Math. 285, Springer, Berlin–New York, 1972. 554 Google Scholar
Hazewinkel, M. (ed.), Encyclopaedia of mathematics, suplement III. Kluwer Academic Publishers, 2002. 679, 685, 703Google Scholar
Helemskii, A. Ya., Banach and locally convex algebras. Translated from Russian by A. West. Oxford Sci. Publ., The Clarendon Press, Oxford University Press, New York, 1993.Google Scholar
Herstein, I. N., Topics in ring theory. The University of Chicago Press, Chicago, 1969. 367, 510Google Scholar
Herstein, I. N., Noncommutative rings. Reprint of the 1968 original. With an afterword by Lance W. Small. Carus Mathematical Monographs 15, Mathematical Association of America, Washington, DC, 1994.Google Scholar
Hille, E., Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, New York, 1948.Google Scholar
Hille, E. and Phillips, R. S., Functional analysis and semi-groups. Third printing of the revised edition of 1957. Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, Providence, RI, 1974.Google Scholar
Hoffman, K., Banach spaces of analytic functions. Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1962.Google Scholar
Iochum, B., Cônes autopolaires et algèbres de Jordan . Lecture Notes in Math. 1049, Springer, Berlin, 1984.Google Scholar
Iochum, B. and Loupias, G. (eds.), Colloque sur les algèbres de Jordan, Montpellier, Octobre 1985 . Ann. Sci. Univ. ‘Blaise Pascal’, Clermont II, Sér. Math . 27 (1991). 674, 679, 681, 685, 702Google Scholar
Iordanescu, R., Jordan structures in analysis, geometry and physics. Editura Academiei Române, Bucharest, 2009. 597 Google Scholar
Isidro, J. M. and Stachó, L. L., Holomorphic automorphism groups in Banach spaces: an elementary introduction . North-Holland Math. Stud. 105, North-Holland Publishing Co., Amsterdam, 1985. xix, 53, 87, 88, 135, 174, 207, 211Google Scholar
Jacobson, N., Lie algebras. Interscience Tracts in Pure and Applied Mathematics 10, Interscience Publishers, New York–London, 1962. 549 Google Scholar
Jacobson, N., Structure of rings. Amer. Math. Soc. Colloq. Publ. 37, Providence, RI, 1964. 500, 559, 598Google Scholar
Jacobson, N., Structure and representations of Jordan algebras . Amer. Math. Soc. Colloq. Publ. 39, Providence, RI, 1968. 472, 594, 597Google Scholar
Jacobson, N., Structure theory of Jordan algebras . University of Arkansas Lecture Notes in Mathematics 5, University of Arkansas, Fayetteville, AR, 1981. 361 Google Scholar
Jameson, G. J. O., Topology and normed spaces. Chapman and Hall, London; Halsted Press [John Wiley & Sons], New York, 1974.Google Scholar
Johnson, W. B. and Lindenstrauss, J. (eds.), Handbook of the geometry of Banach spaces. Vol. 2. North-Holland, Amsterdam, 2003. 671, 681Google Scholar
Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vol. I. Elementary theory . Grad. Stud. Math. 15, American Mathematical Society, Providence, RI, 1997. 330, 366, 459Google Scholar
Kaidi, A., Bases para una teoría de las álgebras no asociativas normadas . PhD thesis, Granada 1978. 597 Google Scholar
Kantor, I. L. and Solodovnikov, A. S., Hypercomplex numbers. An elementary introduction to algebras. Translated from Russian by A. Shenitzer. Springer, New York, 1989.Google Scholar
Kaplansky, I., Rings of operators. Math. Lecture Note Ser., W. A. Benjamin, Inc., New York–Amsterdam, 1968. xxi, 398Google Scholar
Kaplansky, I., Algebraic and analytic aspects of operator algebras. CBMS Regional Conf. Ser. in Math. 1, American Mathematical Society, Providence, RI, 1970.Google Scholar
Kargapolov, M. I. and Merzljakov, Ju. I., Fundamentals of the theory of groups. Translated from the second Russian edition by Robert G. Burns. Grad. Texts in Math. 62, Springer-Verlag, New York–Berlin, 1979. 633 Google Scholar
Kaup, W., McCrimmon, K., and Petersson, H. P. (eds.), Jordan algebras, Proceedings of the conference held in Oberwolfach, Germany, August 9–15, 1992. Walter de Gruyter, Berlin–New York, 1994. 685, 686Google Scholar
Knus, M.-A., Merkurjev, A., Rost, M., and Tignol, J.-P., The book of involutions. Amer. Math. Soc. Colloq. Publ. 44, Providence, RI, 1998.Google Scholar
Lam, T. Y., A first course in noncommutative rings. Second edition. Grad. Texts in Math. 131, Springer, New York, 2001.Google Scholar
Laursen, K. B. and Neumann, M. M., An introduction to local spectral theory. London Math. Soc. Monogr. New Series 20, Clarendon Press, Oxford, 2000. 596 Google Scholar
Li, B., Real operator algebras. World Scientific Publishing Co., Inc., River Edge, NJ, 2003. 549 Google Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. I. Sequence spaces. Ergeb. Math. Grenzgeb. 92, Springer, Berlin–New York, 1977. 261 Google Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. II. Function spaces. Ergeb. Math. Grenzgeb. 97, Springer, Berlin–New York, 1979.Google Scholar
Loos, O., Jordan pairs. Lecture Notes in Math. 460, Springer, Berlin–New York, 1975. 445 Google Scholar
Loos, O., Bounded symmetric domains and Jordan pairs. Lecture Notes, University of California, Irvine, 1977. 211, 337, 441, 444, 454, 460Google Scholar
Loy, R. J. (ed.), Conference on Automatic Continuity and Banach Algebras (Canberra, 1989). Proc. Centre Math. Anal. Austral. Nat. Univ. 21, Austral. Nat. Univ., Canberra, 1989. 672, 681Google Scholar
Martín, M., Índice numérico de un espacio de Banach . PhD thesis, Granada 2000.Google Scholar
Martínez, J., Sobre álgebras de Jordan normadas completas . PhD thesis, Granada 1977. Tesis Doctorales de la Universidad de Granada 149, Secretariado de Publicaciones de la Universidad de Granada, 1977. 597Google Scholar
Mauldin, R. D. (ed.), The Scottish book. Mathematics from the Scottish café. Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. Birkhäuser, Boston, Mass., 1981.Google Scholar
McCrimmon, K., A taste of Jordan algebras . Universitext, Springer, New York, 2004 361, 364, 401, 589, 591, 598Google Scholar
Megginson, R. E., An introduction to Banach space theory. Grad. Texts in Math. 183, Springer, New York, 1998. 7, 220, 340Google Scholar
Meyberg, A., Lectures on algebras and triple systems. Lecture notes, The University of Virginia, Charlottesville, 1972.Google Scholar
Müller, V., Spectral theory of linear operators and spectral systems in Banach algebras. Second edition. Oper. Theory Adv. Appl. 139, Birkhäuser Verlag, Basel, 2007.Google Scholar
Murphy, G. J., C-algebras and operator theory. Academic Press, Inc., Boston, MA, 1990. 330, 408Google Scholar
Myung, H. Ch., Malcev-admissible algebras . Progr. Math. 64, Birkhäuser Boston, Inc., Boston, MA, 1986.Google Scholar
Naimark, M. A., Normed algebras. Translated from the second Russian edition by Leo F. Boron. Third edition. Wolters–Noordhoff Series of Monographs and Textbooks on Pure and Applied Mathematics, Wolters–Noordhoff Publishing, Groningen, 1972. 551 Google Scholar
Ocaña, F. G., El axioma de Sakai en JV-álgebras. PhD thesis, Granada 1979. Tesis Doctorales de la Universidad de Granada 224, Secretariado de Publicaciones de la Universidad de Granada, 1979.Google Scholar
Okubo, S., Introduction to octonion and other non-associative algebras in physics. Montroll Memorial Lecture Ser. Math. Phys. 2, Cambridge University Press, Cambridge, 1995.Google Scholar
Palmer, T. W., Banach algebras and the general theory of ∗-algebras, Volume I, algebras and Banach algebras. Encyclopedia Math. Appl. 49, Cambridge University Press, Cambridge, 1994. xxvi, 650, 651, 652, 654Google Scholar
Palmer, T. W., Banach algebras and the general theory of ∗-algebras, Volume II, ∗-algebras. Encyclopedia Math. Appl. 79, Cambridge University Press, Cambridge, 2001. xvii Google Scholar
Paulsen, V., Completely bounded maps and operator algebras. Cambridge Stud. Adv. Math. 78, Cambridge University Press, Cambridge, 2002. 273 Google Scholar
Pedersen, G., Analysis now. Grad. Texts in Math. 118, Springer, New York, 1989. 330 Google Scholar
Pietsch, A., History of Banach spaces and linear operators. Birkhäuser Boston, Inc., Boston, MA, 2007. 236, 550Google Scholar
Pisier, G., Introduction to operator space theory. London Math. Soc. Lecture Note Ser. 294, Cambridge University Press, Cambridge, 2003.Google Scholar
Przeworska-Rolewicz, D., Linear spaces and linear operators. Institute of Mathematics of the Polish Academy of Sciences, Warsaw, 2007.Google Scholar
Ransford, T., Potential theory in the complex plane. London Math. Soc. Stud. Texts 28, Cambridge University Press, Cambridge, 1995.Google Scholar
Razmyslov, Yu. P., Identities of algebras and their representations. Transl. Math. Monogr. 138, American Mathematical Society, Providence, RI, 1994.Google Scholar
Rickart, C. E., General theory of Banach algebras. The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, NJ–Toronto–London–New York, 1960. 335, 481, 524, 548, 551Google Scholar
Riesz, F. and Sz-Nagy, B., Leçons d’analyse fonctionelle. Cinquième édition. Gauthier-Villars, Paris; Akadémiai Kiadó, Budapest, 1968. 330 Google Scholar
Roch, S., Santos, P. A., and Silbermann, B., Non-commutative Gelfand theories. A tool-kit for operator theorists and numerical analysts . Universitext, Springer London, Ltd., London, 2011.Google Scholar
Rodríguez, A., Contribución a la teoría de las C-álgebras con unidad . PhD thesis, Granada 1974. Tesis Doctorales de la Universidad de Granada 57, Secretariado de Publicaciones de la Universidad de Granada, 1974. 336 Google Scholar
Rodríguez, A., Números hipercomplejos en dimensión infinita . Discurso de ingreso en la Academia de Ciencias Matemáticas, Físico-Químicas y Naturales de Granada, Granada, 1993. 409 Google Scholar
Rolewicz, S., Metric linear spaces. Math. Appl. 20, D. Reidel Publishing Co., Dordrecht; PWN-Polish Scientific Publishers, Warsaw, 1985. 196 Google Scholar
Rose, H. E., Linear algebra. A pure mathematical approach. Birkhäuser Verlag, Basel, 2002.Google Scholar
Rowen, L. H., Ring theory, Volume I . Pure Appl. Math. 127. Academic Press, Inc., Boston, 1988.Google Scholar
Rudin, W., Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. 425, 433Google Scholar
Rudin, W., Functional analysis. Second edition. Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc., New York, 1991.Google Scholar
Rynne, B. P. and Youngson, M. A., Linear functional analysis . Second edition. Springer Undergrad. Math. Ser., Springer London, Ltd., London, 2008.Google Scholar
Sakai, S., C-algebras and W-algebras. Ergeb. Math. Grenzgeb. 60, Springer, New York–Heidelberg, 1971. 19, 329, 331, 339, 399, 421Google Scholar
Sakai, S., Operator algebras in dynamical systems. The theory of unbounded derivations in C-algebras. Encyclopedia Math. Appl. 41, Cambridge University Press, Cambridge, 1991.Google Scholar
Schafer, R. D., An introduction to nonassociative algebras. Corrected reprint of the 1966 original. Dover Publications, Inc., New York, 1995. 208, 360, 361, 401, 545, 652Google Scholar
Schatten, R., Norm ideals of completely continuous operators . Second printing. Ergeb. Math. Grenzgeb. 27, Springer, Berlin–New York, 1970. 409, 481, 494, 524, 531, 532, 533Google Scholar
Sinclair, A. M., Automatic continuity of linear operators. London Math. Soc. Lecture Note Ser. 21, Cambridge University Press, Cambridge–New York–Melbourne, 1976. 499 Google Scholar
Taylor, A. E. and Lay, D. C., Introduction to Functional Analysis. Second edition. John Wiley & Sons, New York–Chichester–Brisbane, 1980.Google Scholar
Tian, J. P., Evolution algebras and their applications. Lecture Notes in Math. 1921, Springer, Berlin, 2008.Google Scholar
Topping, D. M., Jordan algebras of self-adjoint operators. Mem. Amer. Math. Soc. (1965), no. 53. 400Google Scholar
Upmeier, H., Symmetric Banach Manifolds and Jordan C-algebras. North-Holland Math. Stud. 104, North-Holland, Amsterdam, 1985. xix, 52, 53, 87, 135, 174, 207, 211, 597Google Scholar
Upmeier, H. Jordan algebras in analysis, operator theory, and quantum mechanics. CBMS Regional Conf. Ser. in Math. 67, American Mathematical Society, Providence, RI, 1987. 1987. 53, 87, 135, 174, 207, 211Google Scholar
Villena, A. R., Algunas cuestiones sobre las JB∗-álgebras: centroide, centroide extendido y zócalo . PhD thesis, Granada 1990.Google Scholar
Wilansky, A., Modern methods in topological vector spaces. McGraw-Hill International Book Co., New York, 1978.Google Scholar
Wilansky, A., Topology for analysis. Reprint of the 1970 edition. Robert E. Krieger Publishing Co., Inc., Melbourne, FL, 1983.Google Scholar
Wisbauer, R., Modules and algebras: bimodule structure and group actions on algebras. Pitman Monographs Surveys Pure Appl. Math. 81, Longman, Harlow, 1996.Google Scholar
Zelazko, W., Banach algebras. Translated from Polish by Marcin E. Kuczma. Elsevier Publishing Co., Amsterdam–London–New York; PWN-Polish Scientific Publishers, Warsaw, 1973.Google Scholar
Zemánek, J., Properties of the spectral radius in Banach algebras. PhD thesis, Warszawa 1977.Google Scholar
Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P., and Shirshov, A. I., Rings that are nearly associative. Translated from Russian by Harry F. Smith. Pure Appl. Math. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York–London, 1982. 360, 361, 401, 413, 414, 415, 570, 571, 597, 631, 636, 647Google Scholar
Aarnes, J. F., On the Mackey-topology for a von Neumann algebra. Math. Scand . 22 (1968), 87107. 332Google Scholar
Acosta, M. D., An inequality for norm of operators. Extracta Math . 10 (1995), 115–8. 469Google Scholar
Acosta, M. D., Denseness of norm attaining mappings. RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat . 100 (2006), 930. 338Google Scholar
Akemann, C. A., The dual space of an operator algebra. Trans. Amer. Math. Soc . 126 (1967), 286302. xx, 268, 274, 332, 334, 335Google Scholar
Albert, A. A., A theory of trace-admissible algebras. Proc. Nat. Acad. Sci. USA 35 (1949), 317–22. Reprinted in [692], pp. 491–6. 545Google Scholar
Albert, A. A. and Jacobson, N., On reduced exceptional simple Jordan algebras. Ann. of Math . 66 (1957), 400–17. Reprinted in [692], pp. 677–94. 361Google Scholar
Albrecht, E. and Dales, H. G., Continuity of homomorphisms from C∗-algebras and other Banach algebras. In Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981), pp. 375–96, Lecture Notes in Math. 975, Springer, Berlin-New York, 1983. 549Google Scholar
Alfsen, E. M. and Effros, E. G., Structure in real Banach spaces. I, II. Ann. of Math . 96 (1972), 98128; ibid. 96 (1972), 129–73. 19, 398Google Scholar
Allison, B. N., A class of nonassociative algebras with involution containing the class of Jordan algebras. Math. Ann . 237 (1978), 133–56. 555Google Scholar
Allison, B. N., Models of isotropic simple Lie algebras. Comm. Algebra 7 (1979), 1835–75. 555Google Scholar
Allison, B. N. and Faulkner, J. R., The algebra of symmetric octonion tensors. Nova J. Algebra Geom . 2 (1993), 4757. 555Google Scholar
Anquela, J. A., Cabrera, M., and Moreno, A., Eater ideals in Jordan algebras. J. Pure Appl. Algebra 125 (1998), 117. 464Google Scholar
Ara, P., The extended centroid of C -algebras. Archiv. Math . 54 (1990), 358–64. 408Google Scholar
Ara, P., On the symmetric algebra of quotients of a C -algebra. Glasgow Math. J. 32 (1990), 377–9. 408Google Scholar
Arazy, J., An application of infinite-dimensional holomorphy to the geometry of Banach spaces. In Geometrical aspects of functional analysis (1985/86), pp. 122–50, Lecture Notes in Math. 1267, Springer, Berlin, 1987. xix, 87, 135, 174, 207Google Scholar
Arens, R. and Goldberg, G., Quadrative seminorms and Jordan structures on algebras. Linear Algebra Appl . 181 (1993), 269–78. 470Google Scholar
Aupetit, B., Analytic multivalued functions in Banach algebras and uniform algebras. Adv. Math . 44 (1982), 1860. 603Google Scholar
Aupetit, B., Some uses of subharmonicity in functional analysis. In Spectral theory (Warsaw, 1977), pp. 31–7, Banach Center Publ. 8, Polish Acad. Sci. Inst. Math., Warsaw, 1982. 603Google Scholar
Aupetit, B., Inessential elements in Banach algebras. Bull. London Math. Soc . 18 (1986), 493–7. 599Google Scholar
Aupetit, B., Spectral characterization of the radical in Banach and Jordan-Banach algebras. Math. Proc. Cambridge Philos. Soc . 114 (1993), 31–5. 603Google Scholar
Aupetit, B., Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras. J. London Math. Soc . 62 (2000), 917–24. 603Google Scholar
Aupetit, B. and Mouton, H. du T., Trace and determinant in Banach algebras. Studia Math . 121 (1996), 115–36. 601Google Scholar
Aupetit, B. and Zraïbi, A., Propriétés analytiques du spectre dans les algèbres de Jordan-Banach. Manuscripta Math . 38 (1982), 381–6. 596, 597Google Scholar
Bachelis, G. F., Homomorphisms of annihilator Banach algebras. Pacific J. Math . 25 (1968), 229–47. xxv, 584Google Scholar
Bade, W. G., Curtis, P. C. JR., and Sinclair, A. M., Raising bounded groups and splitting of radical extensions of conmmutative Banach algebras. Studia Math . 141 (1) (2000), 8598. 651Google Scholar
Baker, J. W. and Pym, J. S., A remark on continuous bilinear mappings. Proc. Edinburgh Math. Soc . 17 (1970/71), 245–8. 436Google Scholar
Bakić, D. and Guljaš, B., Operators on Hilbert H -modules. J. Operator Theory 46 (2001), 123–37. 557Google Scholar
Balachandran, V. K., Automorphisms of L -algebras. Tôhoku Math. J . 22 (1970), 163–73. 549Google Scholar
Balachandran, V. K., Real L -algebras. Indian J. Pure Appl. Math . 3 (1972), 1224–46. 554Google Scholar
Barton, T. J., Dang, T., and Horn, G., Normal representations of Banach Jordan triple systems. Proc. Amer. Math. Soc . 102 (1988), 551–5. 211, 241Google Scholar
Barton, T. J. and Friedman, Y., Grothendieck’s inequality for JB -triples and applications. J. London Math. Soc . 36 (1987), 513–23. xx, 268, 274, 275, 337, 338, 345, 346Google Scholar
Barton, T. J. and Timoney, R. M., Weak∗-continuity of Jordan triple products and its applications. Math. Scand . 59 (1986), 177–91. xix, 2, 211, 236, 237Google Scholar
Beidar, K. I., Mikhalev, A. V., and Slinko, A. M., A criterion for primeness of nondegenerate alternative and Jordan algebras. Trudy Moskov. Mat. Obshch . 50 (1987), 130–7; translation in Trans. Moscow Math. Soc. 50 (1988), 129–37. xxii, 408, 468Google Scholar
Benkart, G., On inner ideals and ad-nilpotent elements of Lie algebras. Trans. Amer. Math. Soc . 232 (1977), 6181. 600Google Scholar
Benslimane, M. and Boudi, N., Isomorphisms of Jordan-Banach algebras. Extracta Math . 11 (1996), 414–6. 603Google Scholar
Benslimane, M. and Boudi, N., Ring isomorphisms of Jordan-Banach algebras. In Commutative ring theory (Fès, 1995), pp. 105–11, Lect. Notes Pure Appl. Math. 185, Dekker, New York, 1997. 603Google Scholar
Benslimane, M. and Mesmoudi, L., Characterization of commutative normed algebras. In [705], pp. 53–7. 436Google Scholar
Benslimane, M., Mesmoudi, L., and Rodríguez, A., A characterization of commutativity for non-associative normed algebras. Extracta Math . 15 (2000), 121–43. xxii, 436Google Scholar
Berger, M. A. and Wang, Y., Bounded semigroups of matrices. Linear Algebra Appl . 166 (1992), 21–7. 651Google Scholar
Blecher, D. P. and Paulsen, V. I., Multipliers of operator spaces, and the injective envelope. Pacific J. Math . 200 (2001), 117. 273Google Scholar
Bombal, F., On (V) sets and Pełczyński’s property (V). Glasgow Math. J. 32 (1990), 109–20. 266Google Scholar
Bonsall, F. F. and Goldie, A. W., Annihilator algebras. Proc. London Math. Soc . 4 (1954), 154–67. 584Google Scholar
Boudi, N., Marhnine, H., and Zarhouti, C., Additive derivations on Jordan Banach pairs. Comm. Algebra 32 (2004), 3609–25. 466, 603Google Scholar
Boyadjiev, H. N. and Youngson, M. A., Alternators on Banach Jordan algebras. C. R. Acad. Bulgare Sci . 33 (1980), 1589–90. 400Google Scholar
Braun, R., Kaup, W., and Upmeier, H., On the automorphisms of circular and Reinhardt domains in complex Banach spaces. Manuscripta Math . 25 (1978), 97133. 207Google Scholar
Brešar, M., Functional identities: A survey. Contemp. Math . 259 (2000), 93109. 602Google Scholar
Brešar, M. and Villena, A. R., The range of a derivation on a Jordan-Banach algebra. Studia Math . 146 (2001), 177200. 466, 707Google Scholar
Bunce, L. J., The theory and structure of dual JB-algebras. Math. Z. 180 (1982), 525–34. 584, 598Google Scholar
Bunce, L. J., On compact action in JB-algebras. Proc. Edinburgh Math. Soc . 26 (1983), 353–60. 400Google Scholar
Bunce, L. J., Norm preserving extensions in JBW -triple preduals. Quart. J. Math. Oxford 52 (2001), 133–6. 338, 339, 346Google Scholar
Bunce, L. J. and Chu, C.-H., Compact operations, multipliers and Radon-Nikodym property in JB -triples. Pacific J. Math . 153 (1992), 249–65. xx, 275, 346, 450, 459, 461Google Scholar
Bunce, L. J. and Chu, C.-H., Real contractive projections on commutative C -algebras. Math. Z . 226 (1997), 85101. 210Google Scholar
Bunce, L. J., Chu, C.-H., Stachó, L. L., and Zalar, B., On prime JB -triples. Quart. J. Math. Oxford 49 (1998), 279–90. 409Google Scholar
Cabello, J. C. and Cabrera, M., Structure theory for multiplicatively semiprime algebras. J. Algebra 282 (2004), 386421. xxv, 546, 584Google Scholar
Cabello, J. C., Cabrera, M., and Fernández, A., π-complemented algebras through pseudocomplemented lattices. Order 29 (2012), 463–79. 585Google Scholar
Cabello, J. C., Cabrera, M., López, G., and Martindale, W. S. III, Multiplicative semiprimeness of skew Lie algebras. Comm. Algebra 32 (2004), 3487–501. 546Google Scholar
Cabello, J. C., Cabrera, M., and Nieto, E., ε-complemented algebras. J. Algebra 349 (2012), 234–67. 546, 585Google Scholar
Cabello, J. C., Cabrera, M., Rodríguez, A., and Roura, R., A characterization of π-complemented algebras. Comm. Algebra 41 (2013), 3067–79. 585Google Scholar
Cabello, J. C., Cabrera, M., and Roura, R., A note on the multiplicative primeness of degenerate Jordan algebras. Sib. Math. J . 51 (2010), 818–23. 546Google Scholar
Cabello, J. C., Cabrera, M., and Roura, R., π-complementation in the unitisation and multiplication algebras of a semiprime algebra. Comm. Algebra 40 (2012), 3507–31. 546Google Scholar
Cabrera, M., El Marrakchi, A., Martínez, J., and Rodríguez, A.. Bounded differential operators on Hilbert modules and derivations of structurable H -algebras. Comm. Algebra 21 (1993), 2905–45. 559Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Hilbert modules over H -algebras in relation with Hilbert ternary rings. In [734], pp. 33–44. 558Google Scholar
Cabrera, M., Martínez, J., and Rodríguez, A., Hilbert modules revisited: orthonormal bases and Hilbert–Schmidt operators. Glasgow Math. J . 37 (1995), 4554. 557Google Scholar
Cabrera, M. and Mohammed, A. A., Extended centroid and central closure of the multiplication algebra. Comm. Algebra 27 (1999), 5723–36. 546, 576Google Scholar
Cabrera, M. and Mohammed, A. A., A representation theorem for algebras with commuting involutions. Linear Algebra Appl . 306 (2000), 2531. 476Google Scholar
Cabrera, M. and Mohammed, A. A., Extended centroid and central closure of multiplicatively semiprime algebras. Comm. Algebra 29 (2001), 1215–33. 546Google Scholar
Cabrera, M. and Mohammed, A. A., Totally multiplicatively prime algebras. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 1145–62. xxiii, 408, 546, 547, 549Google Scholar
Cabrera, M. and Mohammed, A. A., Algebra of quotients with bounded evaluation of a normed prime algebra. In: Operator theory and Banach algebras. Proceedings of the International Conference in Analysis, Rabat (Moroco), April 12–14, 1999 (eds. Chidami, M., Curto, R., Mbekhta, M., Vasilescu, F.-H. and Zemánek, J.). Theta Found., Bucharest, 2003, pp. 3950. 547Google Scholar
Cabrera, M. and Mohammed, A. A., Algebras of quotients with bounded evaluation of a normed semiprime algebra. Studia Math . 154 (2003), 113–35. 547Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., On primitive Jordan-Banach algebras. In [733], pp. 54–9. 463Google Scholar
Cabrera, M., Moreno, A., and Rodríguez, A., On the behaviour of Jordan-algebra norms on associative algebras. Studia Math . 113 (1995), 81100. xxii, 469, 470, 471, 474Google Scholar
Cabrera, M. and Rodríguez, A., A characterization of the centre of a nondegenerate Jordan algebra. Comm. Algebra 21 (1993), 359–69. 469Google Scholar
Cabrera, M. and Rodríguez, A., Zel’manov’s theorem for nondegenerately ultraprime Jordan-Banach algebras. In [733], pp. 60–5. 462Google Scholar
Cabrera, M. and Villena, A. R., Multiplicative-semiprimeness of nondegenerate Jordan algebras. Comm. Algebra 32 (2004), 39954003. 546Google Scholar
Cao, P. and Turovskii, Yu. V., Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras. Studia Math . 235 (2016), 171208. 603, 652Google Scholar
Cartan, É., Sur les domaines bornes homogenes de l’espace de n variables complexes. Abh. Math. Sem. Univ. Hamburg 11 (1935), 116–62. 210Google Scholar
Cartan, H., Les fonctions de deux variables complexes et le problème de la représentation analytique. J. Math. Pures Appl ., 9 e série, 10 (1931), 1114. 87Google Scholar
Castellón, A. and Cuenca, J. A., Compatibility in Jordan H -triple systems. Boll. Un. Mat. Ital. B 4 (1990), 433–47. 560Google Scholar
Castellón, A. and Cuenca, J. A., Alternative H -triple systems. Comm. Algebra 20 (1992), 3191–206. 561Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Ternary H -algebras. Boll. Un. Mat. Ital. B 6 (1992), 217–28. 559Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Jordan H -triples. In [733], pp. 66–72. 549, 560Google Scholar
Castellón, A., Cuenca, J. A., and Martín, C., Special Jordan H -triple system. Comm. Algebra 28 (2000), 4699–706. 560Google Scholar
Chaperon, M., On the Cauchy–Kowalevski theorem. Enseign. Math . 55 (2009), 359–71. 137Google Scholar
Chu, C.-H. and Iochum, B., Weakly compact operators on Jordan triples. Math. Ann . 281 (1988), 451–8. 335, 340, 341Google Scholar
Chu, C.-H. and Iochum, B., Complementation of Jordan triples in von Neumann algebras. Proc. Amer. Math. Soc . 108 (1990), 1924. 336Google Scholar
Chu, C.-H., Moreno, A., and Rodríguez, A., On prime real JB -triples. In Function spaces (Edwardsville, IL, 1998), pp. 105–9, Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999. 346Google Scholar
Cohen, P. J., Factorization in group algebras. Duke Math. J . 26 (1959), 199205. 659Google Scholar
Crabb, M. J., A new prime C -algebra that is not primitive. J. Funct. Anal . 236 (2006), 630–3. 467Google Scholar
Cuenca, J. A., Sur la théorie de structure des H -algèbres de Jordan non commutatives. In [749], pp. 143–52. 553Google Scholar
Cuenca, J. A., Moufang H -algebras. Extracta Math . 17 (2002), 239–46. 552Google Scholar
Cuenca, J. A., García, A., and Martín, C., Jacobson density for associative pairs and its applications. Comm. Algebra 17 (1989), 2595–610. 560Google Scholar
Cuenca, J. A., García, A., and Martín, C., Prime associative superalgebras with nonzero socle. Algebras Groups Geom . 11 (1994), 359–69. 560Google Scholar
Cuenca, J. A. and Martín, C., Jordan two-graded H -algebras. In [734], pp. 91–100. 559, 560Google Scholar
Cuenca, J. A. and Miguel, F., On a Hopf’s theorem. Preprint 2016. 409Google Scholar
Cuenca, J. A. and Sánchez, A., Structure theory for real noncommutative Jordan H -algebras. J. Algebra 164 (1994), 481–99. 553Google Scholar
Cuntz, J., On the continuity of semi-norms on operator algebras. Math. Ann . 220 (1976), 171–83. 399Google Scholar
Curto, R. E., Spectral theory of elementary operators. In Elementary operators and applications (Blaubeuren, 1991) (Ed. by Mathieu, M.), pp. 352, World Sci. Publ., River Edge, NJ, 1992. 635Google Scholar
D’Amour, A., Quadratic Jordan systems of Hermitian type. J. Algebra 149 (1992), 197233. xxii, 438, 448, 459, 461Google Scholar
D’Amour, A. and McCrimmon, K., The structure of quadratic Jordan systems of Clifford type. J. Algebra 234 (2000), 3189. xxii, 438, 452, 453, 454, 459Google Scholar
Dieudonné, J., Sur le socle d’un anneau et les anneaux simples infinis. Bull. Soc. Math. France 70 (1942), 4675. 598Google Scholar
Dineen, S., Complete holomorphic vector fields on the second dual of a Banach space. Math. Scand . 59 (1986), 131–42. 236Google Scholar
Dineen, S. and Timoney, R. M., The centroid of a JB -triple system. Math. Scand . 62 (1988), 327–42. 346Google Scholar
Dineen, S. and Timoney, R. M., The algebraic metric of Harris on JB -triple systems. Proc. Roy. Irish Acad. Sect. A 90 (1990), 8397. 558Google Scholar
Dixmier, J., Sur les C -algèbres. Bull. Soc. Math. France 88 (1960), 95112. 467Google Scholar
Dixon, P. G., Topologically nilpotent Banach algebras and factorization. Proc. Roy. Soc. Edinburgh Sect A 119 (1991), 329–41. xxvi, 650, 651, 654, 655, 657Google Scholar
Dixon, P. G. and Müller, V., A note on topologically nilpotent Banach algebras. Studia Math . 102 (1992), 269–75. xxvi, 623, 650, 651, 653Google Scholar
Dixon, P. G. and Willis, G. A., Approximate identities in extensions of topologically nilpotent Banach algebras. Proc. Roy. Soc. Edinburgh 122A (1992), 4552. xxvi, 650, 651Google Scholar
Doran, R. S. and Wichmann, J., The Gelfand–Naimark theorems for C -algebras. Enseignement Math . 23 (1977), 153–80. xviiGoogle Scholar
Draper, C., Fernández, A., García, E., and Gómez, M., The socle of a nondegenerate Lie algebra. J. Algebra 319 (2008), 2372–94. 600Google Scholar
Edgar, G. A., An ordering for the Banach spaces. Pacific J. Math . 108 (1983), 8398. 266Google Scholar
Edwards, C. M. and Rüttimann, G. T., A characterization of inner ideals in JB -triples. Proc. Amer. Math. Soc . 116 (1992), 1049–57. 339Google Scholar
El Kinani, A. and Oudadess, M., Un critère généralisé de Le Page et commutativité. C. R. Math. Rep. Acad. Sci. Canada 18 (1996), 71–4. 436Google Scholar
El Marrakchi, A., Sur l’unité approchée des H∗-algèbres structurables avec annulateur zéro. Int. J. Math. Game Theory Algebra 13 (2003), 267–79. 556Google Scholar
Elsner, L., The generalized spectral-radius theorem: an analytic-geometric proof. Linear Algebra Appl . 220 (1995), 151–9. 651Google Scholar
Emmanuele, G., On the Banach spaces with the property (V ) of Pełczyński. Ann. Mat. Pura Appl . 152 (1988), 171–81. 266Google Scholar
Essaleh, A. B. A., Peralta, A. M., and Ramírez, M. I., Pointwise-generalized-inverses of linear maps between C -algebras and JB -triples. Operators and Matrices (to appear). 273, 274Google Scholar
Fernández, A., Banach-Jordan pair. In [741], pp. 57–8. 462, 600Google Scholar
Fernández, A., A Jordan approach to finitary Lie algebras. Quart. J. Math . 67 (2016), 565–71. 600Google Scholar
Fernández, A. and García, E., Algebraic lattices and nonassociative structure. Proc. Amer. Math. Soc . 126 (1998), 3211–21. 584Google Scholar
Fernández, A., García, E., and Gómez, M., The Jordan algebras of a Lie algebra. J. Algebra 308 (2007), 164–77. 600Google Scholar
Fernández, A., García, E., Sánchez, E., and Siles, M., Strong regularity and Hermitian Hilbert triples. Quart. J. Math. Oxford 45 (1994), 4355. 558Google Scholar
Fernández, A. and Golubkov, A. Yu., Lie algebras with an algebraic adjoint representation revisited. Manuscripta Math . 140 (2013), 363–76. 600Google Scholar
Fernández, A., Marhnine, H., and Zarhouti, C., Derivations on Banach-Jordan pairs. Quart. J. Math. Oxford 52 (2001), 269–83. 466, 603Google Scholar
Fernández, A. and Tocón, M. I., Pseudocomplemented semilatices, boolean algebras, and compatible products. J. Algebra 242 (2001), 6091. 584Google Scholar
Fernández, A. and Tocón, M. I., Strongly prime Jordan pairs with nonzero socle. Manuscripta Math . 111 (2003), 321–40. 600Google Scholar
Fernández-Polo, F. J., Garcés, J. J., Peralta, A. M., and Villanueva, I., Tingley’s problem for spaces of trace class operators. Linear Algebra Appl . 529 (2017), 294323. 550Google Scholar
Filippov, V. T., On the theory of Mal’cev algebras. Algebra i Logika 16 (1977), 101–8. 555Google Scholar
Finston, D., On multiplication algebras. Trans. Amer. Math. Soc . 293 (1986), 807–18. 546Google Scholar
Friedman, Y. and Russo, B., Contractive projections on operator triple systems. Math. Scand . 52 (1983), 279311. 210, 331Google Scholar
Garimella, R. V., On continuity of derivations and epimorphisms on some vector-valued group algebras. Bull. Austral. Math. Soc . 56 (1997), 209–15. 596Google Scholar
Giellis, G. R., A characterization of Hilbert modules. Proc. Amer. Math. Soc . 36 (1972), 440–2. 556Google Scholar
Godefroy, G., Épluchabilité et unicité du prédual. Séminaire Choquet, 17e année (1977/78), Initiation á l’analyse, Fasc. 2, Comm. No. 11, 3 pp., Secrétariat Math., Paris, 1978. 8 Google Scholar
Godefroy, G., Parties admissibles d’un espace de Banach. Applications. Ann. Sci. École Norm. Sup. (4) 16 (1983), 109–22. 237, 267Google Scholar
Godefroy, G., Existence and uniqueness of isometric preduals: a survey. In Banach space theory (Iowa City, IA, 1987) (Ed. by Lin, B.-L.), pp. 131–93, Contemp. Math., 85, Amer. Math. Soc., Providence, 1989. 238, 241Google Scholar
Godefroy, G. and Iochum, B., Arens-regularity of Banach algebras and the geometry of Banach spaces. J. Funct. Anal . 80 (1988), 4759. xix, 245, 267, 421Google Scholar
Godefroy, G. and Saab, P., Quelques espaces de Banach ayant les propriétés (V) ou (V ) de A. Pełczyński. C. R. Acad. Sci. Paris Sér. I Math . 303 (1986), 503–6. 245, 266Google Scholar
Godefroy, G. and Saab, P., Weakly unconditionally convergent series in M-ideals. Math. Scand . 64 (1989), 307–18. 266Google Scholar
Godefroy, G. and Talagrand, M., Classes d’espaces de Banach à prédual unique. C. R. Acad. Sci. Paris Sér. I Math . 292 (1981), 323–5. 238Google Scholar
Godefroy, G. and Talagrand, M., Nouvelles classes d’espaces de Banach à prédual unique. Séminaire d’Analyse Fonctionnelle de l’École Polytechnique, 1980/81. 238, 239, 240, 241Google Scholar
Gorin, E. A. and Lin, V. Ja., A condition on the radical of a Banach algebra guaranteeing strong decomposability. (Russian) Mat. Zametki 2 (1967), 589–592; translation in Mathematical Notes 2 (1967), 851–2. 651Google Scholar
Grabiner, S., Finitely generated, Noetherian, and Artinian Banach modules. Indiana Univ. Math. J . 26 (1977), 413–25. 601Google Scholar
Grothendieck, A., Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8 (1953), 179. Reprinted in Resenhas 2 (1996), 401–80. xx, 275, 342, 343Google Scholar
Grothendieck, A., Sur les applications linéaires faiblement compactes d’espaces du type C(K). Canadian J. Math . 5 (1953), 129–73. 334Google Scholar
Gulick, S. L., Commutativity and ideals in the biduals of topological algebras. Pacific J. Math . 18 (1966), 121–37. 268Google Scholar
Haagerup, U., Solution of the similarity problem for cyclic representations of C∗-algebras. Ann. Math . 118 (1983), 215–40. 342Google Scholar
Haagerup, U., The Grothendieck inequality for bilinear forms on C -algebras. Adv. in Math . 56 (1985), 93116. 343, 344Google Scholar
Haagerup, U. and Hanche-Olsen, H., Tomita–Takesaki theory for Jordan algebras. J. Operator Theory 11 (1984), 343–64. 339Google Scholar
Haagerup, U. and Itoh, T., Grothendieck type norms for bilinear forms on C -algebras. J. Operator Theory 34 (1995), 263–83. 342Google Scholar
de la Harpe, P., Classification des L -algèbres semi-simples réelles séparables. C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A1559–61. 554Google Scholar
Harris, L. A., Schwarz’s lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A . 62 (1969), 1014–7. 207Google Scholar
Harris, L. A., A continuous form of Schwarz’s lemma in normed linear spaces. Pacific J. Math . 38 (1971), 635–9. 207Google Scholar
Harris, L. A., Analytic invariants and the Schwarz–Pick inequality. Israel J. Math . 34 (1979), 177–97. 558Google Scholar
Harris, L. A., A generalization of C -algebras. Proc. London Math. Soc . 42 (1981), 331–61. 459Google Scholar
Henriksen, M., A simple characterization of commutative rings without maximal ideals. Amer. Math. Monthly 82 (1975), 502–5. 659Google Scholar
Henson, C. W. and Moore, L. C., Jr., Subspaces of the nonstandard hull of a normed space. Trans. Amer. Math. Soc . 197 (1974), 131–43. 236Google Scholar
Hessenberger, G., Analytic properties of the spectrum in Banach Jordan systems. Collect. Math . 47 (1996), 277–84. 603Google Scholar
Horn, G., Characterization of the predual and ideal structure of a JBW -triple. Math. Scand . 61 (1987), 117–33. xix, 2, 211, 237, 238, 239, 241Google Scholar
Horn, G. and Neher, E., Classification of continuous JBW -triples. Trans. Amer. Math. Soc . 306 (1988), 553–78. 340, 344, 459Google Scholar
Jacobson, N., A note on non-associative algebras. Duke Math. J . 3 (1937), 544–8. 545Google Scholar
James, R. C., Uniformly non-square Banach spaces. Ann. of Math . 80 (1964), 542–50. 261Google Scholar
Jamjoom, F. B., Peralta, A. M., and Siddiqui, A. A., Jordan weak amenability and orthogonal forms on JB -algebras. Banach J. Math. Anal . 9 (2015), 126–45. 346Google Scholar
Jamjoom, F. B., Peralta, A. M., Siddiqui, A. A., and Tahlawi, H. M., Approximation and convex decomposition by extremals and the λ-function in JBW -triples. Quart. J. Math. Oxford 66 (2015), 583603. 346Google Scholar
Jarchow, H., Weakly compact operators on C(K) and C -algebras. In Functional analysis and its applications (Nice, 1986) (Ed. by Hogbe-Nlend, H.), pp. 263–99, ICPAM Lecture Notes, World Sci. Publishing, Singapore, 1988. 274, 335Google Scholar
Jeang, J.-S. and Ko, C.-C., On the commutativity of C -algebras. Manuscripta Math . 115 (2004), 195–8. 401Google Scholar
Ji, G. and Tomiyama, J., On characterizations of commutativity of C -algebras. Proc. Amer. Math. Soc . 131 (2003), 3845–9. 401Google Scholar
Johnson, W. B., Rosenthal, H. P., and Zippin, M., On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math . 9 (1971), 488506. 236Google Scholar
Kadison, R. V., Operator algebras with a faithful weakly-closed representation. Ann. of Math . 64 (1956), 175–81. 19Google Scholar
Kalton, N. J., Rademacher series and decoupling. New York J. Math . 11 (2005), 563–95. 343Google Scholar
Kantrowitz, R. and Neumann, M. M., Automatic continuity of homomorphisms and derivations on algebras of continuous vector-valued functions. Czechoslovak Math. J . 45 ( 120 ) (1995), 747–56. 596Google Scholar
Kaplansky, I., Regular Banach algebras. J. Indian Math. Soc . 12, (1948), 5762. 597Google Scholar
Kaup, W., Jordan algebras and holomorphy. In Functional analysis, holomorphy, and approximation theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978) (Ed. by Machado, S.), pp. 341–65, Lecture Notes in Math., 843, Springer, Berlin, 1981. 211Google Scholar
Kaup, W., Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension. I. Math. Ann . 257 (1981), 463–86. II Math. Ann. 262 (1983), 57–75. 211, 557Google Scholar
Kaup, W., Hermitian Jordan triple systems and the automorphisms of bounded symmetric domains. In [733], pp. 204–14. 210Google Scholar
Kaup, W., On spectral and singular values in JB -triples. Proc. Roy. Irish Acad. Sect. A 96 (1996), 95103. 210Google Scholar
Kaup, W. and Upmeier, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc. Amer. Math. Soc . 58 (1976), 129–33. 207Google Scholar
Kissin, E., Shulman, V. S., and Turovskii, Yu. V., Topological radicals and Frattini theory of Banach Lie algebras. Integral Equations Operator Theory 74 (2012), 51121. 652Google Scholar
Le Page, C., Sur quelques conditions entraînant la commutativité dans les algèbres de Banach. C. R. Acad. Sci. Paris Sér. A–B 265 (1967), A235A237. xxii, 347, 423, 436Google Scholar
Lin, C. S., On commutativity of C -algebras. Glasgow Math. J . 29 (1987), 93–7. 400Google Scholar
Lindenstrauss, J., On operators which attain their norm. Israel J. Math . 1 (1963), 139148. xx, 274, 337, 338Google Scholar
Lindenstrauss, J. and Rosenthal, H. P., The L p -spaces. Israel J. Math . 7 (1969), 325–49. 236Google Scholar
Loos, O., On the socle of a Jordan pair. Collect. Math . 40 (1989), 109–25. 599, 601Google Scholar
Loos, O., Finiteness conditions in Jordan pairs. Math. Z . 206 (1991), 577–87. 558Google Scholar
Loos, O. and Neher, E., Complementation of inner ideals in Jordan pairs. J. Algebra 166 (1994), 255–95. 601Google Scholar
Mackey, M. and Mellon, P., A Schwarz lemma and composition operators. Integral Equations Operator Theory 48 (2004), 511–24. 210Google Scholar
Maouche, A., Extension d’un théorème de Harte et applications aux algèbres de Jordan-Banach. Monatsh. Math . 122 (1996), 205–13. 603Google Scholar
Maouche, A., Diagonalization in Banach algebras and Jordan-Banach algebras. Extracta Math . 19 (2004), 257–60. 603Google Scholar
Martín, M., Norm-attaining compact operators. J. Funct. Anal . 267 (2014), 1585–92. 338Google Scholar
Martínez, J., Derivations of structurable H -algebras. In: Nonassociative algebra and its applications (São Paulo, 1998), pp. 219–27, Lecture Notes in Pure and Appl. Math. 211, Dekker, New York, 2000. 559Google Scholar
Mathieu, M., Weakly compact homomorphisms from C -algebras are of finite rank. Proc. Amer. Math. Soc . 107 (1989), 761–2. 336Google Scholar
Mathieu, M., Elementary operators on prime C -algebras, I. Math. Ann . 284 (1989), 223–44. xxi, 408Google Scholar
Mathieu, M., The symmetric algebra of quotients of an ultraprime Banach algebra. J. Austral. Math. Soc. Ser. A 50 (1991), 7587. 468, 469, 547Google Scholar
Mathieu, M., Review of [869]. MR1853520 (2002k:46123). 466Google Scholar
Mathieu, M. and Runde, V., Derivations mapping into the radical. II. Bull. London Math. Soc . 24 (1992), 485–7. 466Google Scholar
McCrimmon, K., On Herstein’s theorems relating Jordan and associative algebras. J. Algebra 13 (1969), 382–92. 367Google Scholar
McCrimmon, K., A characterization of the radical of a Jordan algebra. J. Algebra 18 (1971), 103–11. 597Google Scholar
McCrimmon, K., The Zel’manov approach to Jordan homomorphisms of associative algebras. J. Algebra 123 (1989), 457–77. 465Google Scholar
Neumann, M. M. and Velasco, M. V., Continuity of epimorphisms and derivations on vector-valued group algebras. Arch. Math. (Basel) 68 (1997), 151–8. 596Google Scholar
Miziolek, J. K., Müldner, T., and Rek, A., On topologically nilpotent algebras. Studia Math . 43 (1972), 4150. xxvi, 650, 651Google Scholar
Mocanu, Gh., Sur certains types de commutativité dans les algèbres de Banach. An. Univ. Bucuresti Mat. 37 (1988), 3641. 436Google Scholar
Mohammadzadeh, S. and Vishki, H. R. E., Arens regularity of module actions and the second adjoint of a derivation. Bull. Aust. Math. Soc . 77 (2008), 465–76. 268Google Scholar
Molnár, L., Modular bases in a Hilbert A-module. Czechoslovak Math. J . 42 (117) (1992), 649–56. 557Google Scholar
Molnár, L., A few conditions for a C -algebra to be commutative. Abstr. Appl. Anal. 2014, Art. ID 705836, 4 pp. 401Google Scholar
Moreno, A., Extending the norm from special Jordan triple systems to their associative envelopes. In Banach algebras’97 (Blaubeuren), pp. 363–75, de Gruyter, Berlin, 1998. xxiii, 475, 476Google Scholar
Moreno, A., The triple-norm extension problem: the nondegenerate complete case. Studia Math . 136 (1999), 91–7. xxiii, 475, 476Google Scholar
Moreno, A., Some recent results about the norm extension problem. In [705], pp. 125–31. xxiii, 462, 474, 475Google Scholar
Moreno, A. and Rodríguez, A., The norm extension problem: positive results and limits. II Congress on Examples and Counterexamples in Banach Spaces (Badajoz, 1996). Extracta Math . 12 (1997), 165–71. 462, 473, 474Google Scholar
Moreno, A. and Rodríguez, A., Algebra norms on tensor products of algebras, and the norm extension problem. Linear Algebra Appl . 269 (1998), 257305. xxiii, 472, 473, 474, 475Google Scholar
Müller, V., Nil, nilpotent and PI-algebras. In [1189], pp. 259–65. xxvi, 651Google Scholar
Neufang, M., On Mazur’s property and property (X). J. Operator Theory 60 (2008), 301–16. 238, 239Google Scholar
Ogasawara, T., A theorem on operator algebras. J. Sci. Hiroshima Univ. Ser. A . 18 (1955), 307–9. 400Google Scholar
Osborn, J. M. and Racine, M. L., Jordan rings with nonzero socle. Trans. Amer. Math. Soc . 251 (1979), 375–87. 598Google Scholar
Oudadess, M., Commutativité de certaines algèbres de Banach. Bol. Soc. Mat. Mexicana 28 (1983), 914. 436Google Scholar
Pedersen, G. K. and Størmer, E., Traces on Jordan algebras. Canad. J. Math . 34 (1982), 370–3. 339Google Scholar
Pełczyński, A., Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Acad. Polon. Sci . 10 (1962), 641–8. 266Google Scholar
Peralta, A. M., Little Grothendieck’s theorem for real JB -triples. Math. Z . 237 (2001), 531–45. 337, 346Google Scholar
Peralta, A. M., New advances on the Grothendieck’s inequality problem for bilinear forms on JB -triples. Math. Inequal. Appl . 8 (2005), 721. 346Google Scholar
Peralta, A. M., Some remarks on weak compactness in the dual space of a JB -triple. Tôhoku Math. J . 58 (2006), 149–59. 335, 340Google Scholar
Peralta, A. M. and Rodríguez, A., Grothendieck’s inequalities for real and complex JBW -triples. Proc. London Math. Soc . 83 (2001), 605–25. xx, 268, 274, 338, 340, 341, 342, 344, 345, 346Google Scholar
Peralta, A. M. and Rodríguez, A., Grothendieck’s inequalities revisited. In [1141], pp. 409–23. 346Google Scholar
Pérez de Guzmán, I., Structure theorems for alternative H -algebras. Math. Proc. Cambridge Philos. Soc. 94 (1983), 437–46. xxv, 549Google Scholar
Pérez de Guzmán, I., Annihilator alternative algebras. Pacific J. Math. 107 (1983), 8994. 584Google Scholar
Pfitzner, H., L-summands in their biduals have Pełczyński’s property (V). Studia Math. 104 (1993), 91–8. xix, 245, 267Google Scholar
Pfitzner, H., Separable L-embedded Banach spaces are unique preduals. Bull. Lond. Math. Soc. 39 (2007), 1039–44. 241Google Scholar
Pfitzner, H., Phillips’ lemma for L-embedded Banach spaces. Arch. Math. (Basel) 94 (2010), 547–53. 267Google Scholar
Pfitzner, H., A well-known criterion of Pełczyński’s Property (V). Private communication, September 2014. xix, 2, 245, 266, 267Google Scholar
Pfitzner, H., Predual uniqueness coming from the generalized property (X) à la Godefroy–Talagrand. Private communication, April 2017. 238, 241Google Scholar
Phillips, R. S., On symplectic mappings of contraction operators. Studia Math. 31 (1968) 1527. 207Google Scholar
Pinter-Lucke, J., Commutativity conditions for rings: 1950–2005. Expo. Math. 25 (2007), 165–74. 401Google Scholar
Pisier, G., Grothendieck’s theorem for noncommutative C -algebras, with an appendix on Grothendieck’s constants. J. Funct. Anal. 29 (1978), 397415. 342, 343Google Scholar
Pisier, G., Grothendieck’s theorem, past and present. Bull. Amer. Math. Soc. 49 (2012), 237323. xx, 342, 343Google Scholar
Poliquin, R. A. and Zizler, V. E., Optimization of convex functions on w -compact sets. Manuscripta Math. 68 (1990), 249270. 338Google Scholar
Pritchard, F. L., Ideals in the multiplication algebra of a nonassociative K-algebra. Comm. Algebra 21 (1993), 4541–59. 546Google Scholar
Pyatetskii-Shapiro, I. I., On a problem proposed by E. Cartan. Dokl. Akad. Nauk SSSR 124 (1959), 272–3. 210Google Scholar
Pym, J. S., The convolution of functionals on spaces of bounded functions. Proc. London Math. Soc. 15 (1965), 84104. 267Google Scholar
Randrianantoanina, N., Pełczyński’s property (V) for symmetric operator spaces. Proc. Amer. Math. Soc. 125 (1997), 801–6. 267Google Scholar
Robbin, J. W., On the existence theorem for differential equations. Proc. Amer. Math. Soc. 19 (1968), 1005–6. 137Google Scholar
Rodríguez, A., La continuidad del producto de Jordan implica la del ordinario en el caso completo semiprimo. In: Contribuciones en probabilidad, estadística matemática, enseñanza de la matemática y análisis, pp. 280–8, Secretariado de Publicaciones de la Universidad de Granada, Granada, 1979. xxiii, 474Google Scholar
Rodríguez, A., A note on Arens regularity. Quart. J. Math. Oxford 38 (1987), 91–3. 267, 268Google Scholar
Rodríguez, A., On the strong topology of a JBW -triple. Quart. J. Math. Oxford 42 (1991), 99103. xx, 274, 335, 337, 338, 339Google Scholar
Rodríguez, A., Non-associative normed algebras: geometric aspects. In [1189], pp. 299–311. 421, 462Google Scholar
Rodríguez, A., Estructuras de Jordan en Análisis. Rev. Real Acad. Cienc. Exact. Fís. Natur. Madrid 88 (1994), 309–17. 462Google Scholar
Rodríguez, A. and Velasco, M. V., Continuity of homomorphisms and derivations on normed algebras which are tensor products of algebras with involution. Rocky Mountain J. Math. 32 (2002), 1045–55. xxiii, 474, 475Google Scholar
Rodríguez, A. and Villena, A. R., Centroid and extended centroid of JB -algebras, In [734], pp. 223–32. 408Google Scholar
Rosentahl, P. and Soltysiak, A., Formulas for the joint spectral radius of non-commuting Banach algebra elements. Proc. Amer. Math. Soc. 123 (9) (1995), 2705–8. 651Google Scholar
Ruckle, W. H., The infinite sum of closed subspaces of an F-space. Duke Math. J. 31 (1964), 543–54. 584Google Scholar
Runde, V., Review of [462]. MR1706325 (2000f:46067). 596Google Scholar
Russo, B., Derivations and projections on Jordan triples: an introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis. In Advanced courses of mathematical analysis V, pp. 118227, World Sci. Publ., Hackensack, NJ, 2016. 346Google Scholar
Sakai, S., A characterization of W -algebras. Pacific J. Math. 6 (1956), 763–73. 19Google Scholar
Sakai, S., Weakly compact operators on operator algebras. Pacific J. Math. 14 (1964), 659–64. 274, 336Google Scholar
Sakai, S., On topologies of finite W -algebras. Illinois J. Math. 9 (1965), 236–41. 334Google Scholar
Saworotnow, P. P., A generalized Hilbert space. Duke Math. J. 35 (1968), 191–7. 556Google Scholar
Saworotnow, P. P., Trace-class and centralizers of an H -algebra. Proc. Amer. Math. Soc. 26 (1970), 101–4. 550Google Scholar
Saworotnow, P. P. and Friedell, J. C., Trace-class for an arbitrary H -algebra. Proc. Amer. Math. Soc. 26 (1970), 95100. 550Google Scholar
Schafer, R. D., On structurable algebras. J. Algebra 92 (1985), 400–12. 555Google Scholar
Schafer, R. D., Invariant forms on central simple structurable algebras. J. Algebra 122 (1989), 112–7. 556Google Scholar
Schatten, R., The cross-space of linear transformations. Ann. of Math. 47 (1946), 7384. 550Google Scholar
Schatten, R. and von Neumann, J., The cross-space of linear transformations. II. Ann. of Math. 47 (1946), 608–30. 550Google Scholar
Schatten, R. and von Neumann, J., The cross-space of linear transformations. III. Ann. of Math. 49 (1948), 557–82. 550Google Scholar
Sherman, S., Order in operator algebras. Amer. J. Math. 73 (1951), 227–32. 400Google Scholar
Shestakov, I. P., Speciality and deformations of algebras. In: Algebra: Proceedings of the International Algebraic Conference on the Occasion of the 90th Birthday of A. G. Kurosh (Moscow, 1998), pp. 345–56, de Gruyter, Berlin, 2000. xxii, 470Google Scholar
Shulman, V. S., On invariant subspaces of Volterra operators. (Russian) Funk. Anal. i Prilozen 18 (1984), 84–5. xxvi, 651Google Scholar
Shulman, V. S., Invariant subspaces and spectral mapping theorems. In [1189], pp. 313–25. 651Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals. I. Basic properties, tensor products and joint quasinilpotence. In Topological algebras, their applications, and related topics (Ed. by Jarosz, K. and Soltysiak, A.), pp. 293333, Banach Center Publ. 67, Polish Acad. Sci., Warsaw, 2005. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals, II. Applications to spectral theory of multiplication operators. In Elementary operators and their applications (Belfast, 2009) (Ed. by Curto, R. E. and Mathieu, M.), pp. 45114, Oper. Theory Adv. Appl., 212, Birkhäuser/Springer Basel AG, Basel, 2011. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals and the joint spectral radius. (Russian) Funktsional. Anal. i Prilozhen. 46 (2012), 6182; translation in Funct. Anal. Appl. 46 (2012), 287–304. 652Google Scholar
Shulman, V. S. and Turovskii, Yu. V., Topological radicals, V. From algebra to spectral theory. In Algebraic methods in functional analysis. The Victor Shulman anniversary volume (Ed. by Todorov, I. G. and Turowska, L.), pp. 171280, Oper. Theory Adv. Appl., 233, Birkhäuser/Springer Basel AG, Basel, 2013. 652Google Scholar
Simons, S., On the Dunford–Pettis property and Banach spaces that contain c 0 . Math. Ann. 216 (1975), 225–31. 266Google Scholar
Sinclair, A. M., Homomorphisms from C -algebras. Proc. London Math. Soc. 29 (1974), 435–52. Corrigendum: Proc. London Math. Soc. 32 (1976), 322. 548Google Scholar
Sinclair, A. M. and Tullo, A. W., Noetherian Banach algebras are finite dimensional. Math. Ann. 211 (1974), 151–3. 601Google Scholar
Smirnov, O. N., Simple and semisimple structurable algebras. (Russian) Algebra i Logika 29 (1990), 571–96; translation in Algebra and Logic 29 (1990), 377–94. 555Google Scholar
Smith, J. F., The structure of Hilbert modules. J. London Math. Soc. 8 (1974), 741–9. 556Google Scholar
Smith, R. R. and Ward, J. D., M-ideal structure in Banach algebras. J. Funct. Anal. 27 (1978), 337–49. 19Google Scholar
Soltysiak, A., On the joint spectral radii of commuting Banach algebra elements. Studia Math. 105 (1993), 93–9. 651Google Scholar
Stacey, P. J., Type I 2 JBW-algebras. Quart. J. Math. Oxford 33 (1982), 115–27. 416Google Scholar
Stachó, L. L., A short proof of the fact that biholomorphic automorphisms of the unit ball in certain L p spaces are linear. Acta Sci. Math. (Szeged) 41 (1979), 381–3. 207Google Scholar
Stachó, L. L., On nonlinear projections of vector fields. In Convex analysis and chaos (Sakado, 1998), pp. 4754, Josai Math. Monogr. 1, Josai Univ., Sakado, 1999. 207Google Scholar
Stampfli, J. G., The norm of a derivation. Pacific J. Math. 33 (1970), 737–47. 550Google Scholar
Steptoe, A. C. P., JC -triples and inner ideals in universally reversible JC -algebras. Quart. J. Math. 56 (2005), 397402. 460Google Scholar
Stern, J., Some applications of model theory in Banach space theory. Ann. Math. Logic 9 (1976), 49121. 236Google Scholar
Stone, M. H., Boundedness properties in function-lattices. Canadian J. Math. 1 (1949), 176–86. 421 Google Scholar
Takesaki, M., On the conjugate space of operator algebra. Tôhoku Math. J. 10 (1958), 194203. 334Google Scholar
Taylor, D. C., The strict topology for double centralizer algebras. Trans. Amer. Math. Soc. 150 (1970) 633–43. 400Google Scholar
Tullo, A. W., Conditions on Banach algebras which imply finite dimensionality. Proc. Edinburgh Math. Soc. 20 (1976), 15. 598Google Scholar
Turovskii, Yu. V., Spectral properties of elements of normed algebras, and invariant subspaces. (Russian) Funktsional. Anal. i Prilozhen. 18 (1984), 77–8; translation in Funct. Anal. Appl. 18 (1984), 152–4. 651Google Scholar
Turovskii, Yu. V. and Shulman, V. S., Radicals in Banach algebras, and some problems in the theory of radical Banach algebras. (Russian) Funktsional. Anal. i Prilozhen. 34 (2001), no. 4, 8891; translation in Funct. Anal. Appl. 35 (2001), 312–4. 652Google Scholar
Turovskii, Yu. V. and Shulman, V. S., Topological radicals and the joint spectral radius. (Russian) Funktsional. Anal. i Prilozhen. 46 (2012), 6182; translation in Funct. Anal. Appl. 46 (2012), 287–304. 652Google Scholar
Ülger, A., Weakly compact bilinear forms and Arens regularity. Proc. Amer. Math. Soc. 101 (1987), 697704. 268Google Scholar
Umegaki, H., Weak compactness in an operator space. Kōdai Math. Sem. Rep. 8 (1956), 145–51. 334Google Scholar
Unsain, I., Classification of the simple separable real L -algebras. J. Differential Geometry 7 (1972), 423–51. 554Google Scholar
Upmeier, H., Über die Automorphismengruppen von Banach-Mannigfaltigkeiten mit invarianter Metrik. Math. Ann. 223 (1976), 279–88. 174Google Scholar
Upmeier, H., Remarks on the Campbell–Hausdorff formula for holomorphic vector fields. Private communication, June 2017. xix, 174Google Scholar
Vigué, J.-P., Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. Ann. Sci. École Norm. Sup. (4) 9 (1976), 203–81. xix, 87, 159, 174, 211Google Scholar
Vigué, J.-P., Les domaines bornés symétriques d’un espace de Banach complexe et les systémes triples de Jordan. Math. Ann. 229 (1977), 223–31. 211Google Scholar
Vigué, J.-P., Sur la décomposition d’un domaine borné symétrique en produit continu de domaines bornés symétriques irréductibles. Ann. Sci. École Norm. Sup. (4) 14 (1981), 453–63. 241Google Scholar
Villena, A. R., Continuity of derivations on a complete normed alternative algebra. J. Inst. Math. Comput. Sci. Math. Ser. 3 (1990), 99106. 548Google Scholar
Viola Devapakkiam, C., Hilbert space methods in the theory of Jordan algebras. I. Math. Proc. Cambridge Philos. Soc. 78 (1975), 293300. xxv, 552Google Scholar
Viola Devapakkiam, C. and Rema, P. S., Hilbert space methods in the theory of Jordan algebras. II. Math. Proc. Cambridge Philos. Soc. 79 (1976), 307–19. xxv, 552Google Scholar
Weaver, N., A prime C -algebra that is not primitive. J. Funct. Anal. 203 (2003), 356–61. 467Google Scholar
Wilkins, T. J. D., Spectrum-finite ideals of Jordan-Banach algebras. J. London Math. Soc. 54 (1996), 359–68. 601Google Scholar
Yeadon, F. J., A note on the Mackey topology of a von Neumann algebra. J. Math. Anal. Appl. 45 (1974), 721–2. 336Google Scholar
Yood, B., Closed prime ideals in topological rings. Proc. London Math. Soc. 24 (1972), 307–23. 583, 584Google Scholar
Youngson, M. A., Review of [710]. Bull. Lond. Math. Soc. 44 (2012), 1304–7. xixGoogle Scholar
Zalar, B., Continuity of derivations on Mal’cev H -algebras. Math. Proc. Cambridge Philos. Soc. 110 (1991), 455–9. 548Google Scholar
Zalar, B., On derivations of H -algebras. University of Ljubljana, Preprint Series of the Department of Mathematics, Vol. 29 (1991), 356. 548Google Scholar
Zalar, B., A note on the definition of a nonassociative H -triple. University of Ljubljana, Preprint Series of the Department of Mathematics, Vol. 30 (1992), 361. 561Google Scholar
Zalar, B., Continuity of derivation pairs on alternative and Jordan H -triples. Boll. Un. Mat. Ital. B 7 (1993), 215–30. 559Google Scholar
Zalar, B., Theory of Hilbert triple systems. Yokohama Math. J. 41 (1994), 95126. 558Google Scholar
Zel’manov, E. I., Jordan algebras with finiteness conditions. Algebra Logic 17 (1978), 450–7. 562Google Scholar
Zel’manov, E. I., On prime Jordan algebras. Algebra Logic 18 (1979), 162–75. 364, 437Google Scholar
Zel’manov, E. I., Lie algebras with algebraic associated representation. (Russian) Mat. Sb. (N.S.) 121 ( 163 ) (1983), 545–61; translation in Math. USSR-Sb. 49 (1984), 537–52. 658Google Scholar
Zel’manov, E. I., Primary Jordan triple systems. Sibirsk. Mat. Zh. 24 (1983), 2337. xxii, 437, 438, 459Google Scholar
Zel’manov, E. I., Primary Jordan triple systems. II. Sibirsk. Mat. Zh. 25 (1984), 5061. xxii, 437, 438, 447, 459Google Scholar
Zel’manov, E. I., Lie algebras with a finite grading. Math. USSR Sb. 52 (1985), 347–85. 600Google Scholar
Zel’manov, E. I., On Engel Lie algebras. Soviet Math. Dokl. 35 (1987), 44–7. 658Google Scholar
Zizler, V., On some extremal problems in Banach spaces. Math. Scand. 32 (1973), 214–24. xx, 274, 337Google Scholar
Abraham, R., Marsden, J. E., and Ratiu, T., Manifolds, tensor analysis, and applications. Second edition. Applied Mathematical Sciences, 75. Springer-Verlag, New York, 1988. 135 Google Scholar
Alvermann, K., Normierte nichtkommutative Jordan-Algebren vom Typ I. PhD thesis, Braunschweig 1982. 421 Google Scholar
Behrends, E., M-structure and the Banach–Stone theorem. Lecture Notes in Math. 736, Springer, Berlin, 1979. 350, 351, 398Google Scholar
Bierstedt, K. D., Bonet, J., Maestre, M., and Schmets, J. (eds.), Recent progress in functional analysis. Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia, Valencia, Spain, July 3–7, 2000. North Holland Math. Studies 189, Elsevier, Amsterdam 2001. 679, 708Google Scholar
Bonfiglioli, A. and Fulci, R., Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin. Lecture Notes in Math. 2034, Springer, Heidelberg, 2012. 154, 155, 174Google Scholar
Bourbaki, N., Éléments de mathématique: groupes et algèbres de Lie. Chapitres 2 et 3. Springer-Verlag, Berlin, 2006. 154, 155, 174Google Scholar
Cabrera, M., H-álgebras no asociativas reales. H-álgebras de Malcev complejas y reales . PhD thesis, Granada 1987. Tesis Doctorales de la Universidad de Granada, Secretariado de Publicaciones de la Universidad de Granada, 1988. 552, 555Google Scholar
Cartan, H., Sur les groupes de transformations analytiques. Act. Sci. Ind. 198, Hermann, Paris, 1935. 87 Google Scholar
Cartan, H., Cours de calcul différentiel. Second edition. Hermann, Paris, 1977. 53 Google Scholar
Chaperon, M., Calcul différentiel et calcul intégral. Second edition. Dunod, Paris, 2008. 53 Google Scholar
Coleman, R., Calculus on normed vector spaces. Universitext. Springer, New York, 2012. 53, 135, 136Google Scholar
Conway, J. B., Functions of one complex variable. Second edition. Grad. Texts in Math. 11. Springer-Verlag, New York-Berlin, 1978. 44, 55, 58, 101, 185Google Scholar
Dales, H. G., Dashiell, F. K., Jr., Lau, A. T.-M., and Strauss, D., Banach Spaces of Continuous Functions as Dual Spaces. CMS Books Math., Springer, New York, 2016. 421 Google Scholar
Diestel, J., Sequences and series in Banach spaces. Grad. Texts in Math. 92. Springer-Verlag, New York, 1984. 239, 245, 253, 258, 266, 267, 279Google Scholar
Dieudonné, J., Éléments d’analyse. Tome I. Fondements de l’analyse moderne . Third edition. Translated from the English by D. Huet. With a foreword by Gaston Julia. Cahiers Scientifiques XXVIII. Gauthier-Villars, Paris, 1981. 53, 135, 136Google Scholar
Dieudonné, J., Éléments d’analyse . Tome II: Chapitres XII à XV. Cahiers Scientifiques XXXI Gauthier-Villars, Paris, 1968. 335 Google Scholar
Dineen, S., Complex analysis in locally convex spaces. North-Holland Math. Stud. 57. North-Holland Publishing Co., Amsterdam, 1981. 53 Google Scholar
Dineen, S., Complex analysis on infinite-dimensional spaces. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 1999. xxvi, 53Google Scholar
Doran, R. S. and Wichmann, J., Approximate identities and factorization in Banach modules . Lecture Notes in Math. 768, Springer, Berlin, 1979. xxvi, 651, 652Google Scholar
Fernández, A., Teoremas de Wedderburn-Zorn en álgebras alternativas normadas completas, PhD thesis, Universidad de Granada 1983. 583, 584Google Scholar
Fernández, A., Jordan techniques in Lie algebras. Book in progress. 600Google Scholar
Franzoni, T. and Vesentini, E., Holomorphic maps and invariant distances . North-Holland Math. Stud. 69, North-Holland Publishing Co., Amsterdam, 1980. 53, 87Google Scholar
Hervé, M., Analyticity in infinite-dimensional spaces. de Gruyter Studies in Mathematics, 10. Walter de Gruyter & Co., Berlin, 1989. 53 Google Scholar
Horváth, J., Topological vector spaces and distributions. Volume I. Addison-Wesley Publishing Co., Reading, Massachusetts-London-Don Mills, Ontario, 1966. 7, 290Google Scholar
Istrǎtescu, V. I., Inner product structures. Theory and applications. Mathematics and its Applications, 25. D. Reidel Publishing Co., Dordrecht, 1987. 551, 557Google Scholar
Jarchow, H., Locally convex spaces. Mathematische Leitfäden. B. G. Teubner, Stuttgart, 1981. 335 Google Scholar
Johnstone, P. T., Stone spaces. Reprint of the 1982 edition. Cambridge Studies in Advanced Mathematics, 3. Cambridge University Press, Cambridge, 1986. 421 Google Scholar
Jungers, R., The joint spectral radius. Theory and applications. Lecture Notes in Control and Information Sciences, 385. Springer-Verlag, Berlin, 2009. 651 Google Scholar
Kadets, V., Martín, M., Merí, J., and Pérez, A., Spear operators between Banach spaces . Lecture Notes in Math., Springer. 209 Google Scholar
Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vol. II. Advanced theory . Grad. Stud. Math. 16, American Mathematical Society, Providence, RI, 1997. 19 Google Scholar
Kelley, J. L. and Namioka, I., Linear topological spaces. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, NJ, 1963. 288 Google Scholar
Koecher, M., An elementary approach to bounded symmetric domains, Lecture Notes (Rice University, Houston, TX, 1969). 211 Google Scholar
Lang, S., Differential and Riemannian manifolds . Third edition. Grad. Texts in Math. 160. Springer-Verlag, New York, 1995. 135 Google Scholar
Lee, J. M., Introduction to smooth manifolds . Second Edition. Grad. Texts in Math. 218. Springer, New York, 2013. 135 Google Scholar
Lelong-Ferrand, J. and Arnaudiès, J. M., Cours de mathématiques. Tome 2: Analyse . Fourth edition. Dunod, Paris, 1977. 53 Google Scholar
Mellon, P., An introduction to bounded symmetric domains . Textos de Matemática. Série B. Universidade de Coimbra, Departamento de Matemática, Coimbra, 2000. 210, 211Google Scholar
Moreno, A., Álgebras de Jordan-Banach primitivas, PhD thesis, Universidad de Granada 1995. 470 Google Scholar
Mujica, J., Complex analysis in Banach spaces . Dover Publications, Inc. Mineola, New York, 2010. 53, 87Google Scholar
Narasimhan, R., Several complex variables . Chicago Lectures in Mathematics. The University of Chicago Press, Chicago and London, 1971. 87, 207Google Scholar
Neher, E., Jordan triple systems by the grid approach. Lecture Notes in Math. 1280, Springer-Verlag, Berlin, 1987. 557 Google Scholar
Pedersen, G. K., C-algebras and their automorphism groups. London Math. Soc. Monogr. 14, Academic Press, London-New York, 1979. 408 Google Scholar
Pérez de Guzmán, I., Álgebras alternativas normadas. Teorema de estructura para H-álgebras alternativas . PhD thesis, Granada 1977. Tesis Doctorales de la Universidad de Granada 266, Secretariado de Publicaciones de la Universidad de Granada, 1980. 549 Google Scholar
Reich, S. and Shoikhet, D., Nonlinear semigroups, fixed points, and geometry of domains in Banach spaces. Imperial College Press, London, 2005. 79, 87, 88, 135Google Scholar
Reutenauer, C., Free Lie algebras. London Mathematical Society Monographs. New Series, 7. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993. 154, 174Google Scholar
Ringrose, J. R., Compact non-self-adjoint operators. Van Nostrand Reinhold Co., London, 1971. 481, 524Google Scholar
Saitô, K. and Wright, J. D. M., Monotone complete C-algebras and generic dynamics. Springer Monographs in Mathematics. Springer, London, 2015. 19 Google Scholar
Singer, I., Bases in Banach spaces . I. Die Grundlehren der mathematischen Wissenschaften, Band 154. Springer-Verlag, New York-Berlin, 1970. 239 Google Scholar
Takesaki, M., Theory of operator algebras. I. Reprint of the first (1979) edition. Encyclopaedia of Mathematical Sciences, 124. Operator Algebras and Noncommutative Geometry, 5. Springer-Verlag, Berlin, 2002. 332, 334, 335Google Scholar
Upmeier, H., Über die Automorphismengruppen beschränkter Gebiete in Banachräumen. PhD thesis, Tübingen 1975. 174 Google Scholar
Vigué, J.-P., Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. PhD thesis, Publication Mathématique d’Orsay, 1976. 87, 135, 174, 211Google Scholar
Willard, S., General topology. Reprint of the 1970 original [Addison-Wesley, Reading, MA; MR0264581]. Dover Publications, Inc., Mineola, NY, 2004. 87, 280Google Scholar
Zemánek, J. (Editor), Functional analysis and operator theory (Warsaw, 1992). Banach Center Publ., 30, Polish Acad. Sci., Warsaw, 1994. 665, 707, 709Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×