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Published online by Cambridge University Press:  08 July 2022

Aurelian Gheondea
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Bilkent University, Ankara
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An Indefinite Excursion in Operator Theory
Geometric and Spectral Treks in Kreĭn Spaces
, pp. 476 - 483
Publisher: Cambridge University Press
Print publication year: 2022

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References

Adamyan, V. M., Arov, D. Z., and KreĬn, M. G.: Analytic properties of Schmidt pairs of Hankel operators and the generalized Schur-Takagi problem [Russian], Mat. Sbornik, 86(1971), 3373.Google Scholar
Adamyan, V. M., Arov, D. Z., and KreĬn, M. G.: Infinite block Hankel operators and some related continuation problems [Russian], Izv. Akad. Nauk Armyan. SSR Ser. Mat., 6(1971), 87112.Google Scholar
Akhiezer, N. I. and Glazman, I. M.: The Theory of Operators in Hilbert Space [Russian], 3rd revised edition, Vyshcha Shkola, Kharkov 1978; English translation., Pitman, Boston, MA 1981.Google Scholar
Ando, T.: Linear Operators in Kreĭn Spaces, Lecture Notes, Hokkaido University, Sapporo 1979.Google Scholar
Arocena, R., Azizov, T. Ya., Dijksma, A., and Marcantognini, S. A. M.: On commutant lifting with finite defect. J. Operator Theory, 35(1996), no. 1, 117132.Google Scholar
Arocena, R., Azizov, T. Ya., Dijksma, A., and Marcantognini, S. A. M.: On commutant lifting with finite defect. II. J. Funct. Anal., 144(1997), no. 1, 105116.CrossRefGoogle Scholar
Arsene, Gr., Constantinescu, T., and Gheondea, A.: Lifting of operators and prescribed negative squares, Michigan Math. J., 34(1987), 201216.Google Scholar
Arsene, Gr. and Gheondea, A.: Completing matrix contractions, J. Operator Theory, 7(1982), 179189.Google Scholar
Azizov, T. Ya.: On the Theory of Isometric and Symmetric Operators in Spaces with an Indefinite Metric [Russian], Deposited VINITI, 29(1982), 34203482.Google Scholar
Azizov, T. Ya. and Iokhvidov, I. S.: Foundations of the Theory of Linear Operators in Spaces with Indefinite Metric [Russian], Nauka, Moscow 1986; English translation, Linear Operators in Spaces with Indefinite Metric, Wiley, New York 1989.Google Scholar
Ball, J. A. and Helton, J. W.: Factorization results related to shifts in an indefinite metric, Integral Equations Operator Theory, 5(1982), 632658.Google Scholar
Ball, J. A. and Helton, J. W.: A Beurling-Lax theorem for the Lie group U (m, n) which contains most classical interpolation theory, J. Operator Theory, 9(1983), 107142.Google Scholar
Ball, J. A. and Helton, J. W.: Beurling-Lax representations using classical Lie groups with many applications. II: GL(n, ℂ) and the Wiener-Hopf factorization, Integral Equations Operator Theory, 7(1984), 291309.CrossRefGoogle Scholar
Ball, J. A. and Helton, J. W.: Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrizations of the set of all solutions, Integral Equations and Operator Theory, 9(1985), 105203.Google Scholar
Ball, J. A. and Helton, J. W.: Beurling-Lax representations using classical Lie groups with many applications. III: Groups preserving two bilinear forms, Am. J. Math., 108(1986), 95174.Google Scholar
Ball, J. A. and Helton, J. W.: Beurling-Lax representations using classical Lie groups with many applications. IV: GL(n, ℝ), SL(n, ℂ), and a solvable group, J. Funct. Anal., 69(1986), 178206.Google Scholar
Beurling, A.: On two problems concerning linear transformations in Hilbert space, Acta Math., 81(1949), 239255.Google Scholar
Bognár, J.: Indefinite Inner Product Spaces, Springer-Verlag, Berlin 1974.CrossRefGoogle Scholar
Bognár, J.: A proof of the spectral theorem for J-positive operators, Acta Sci. Math. (Szeged), 45(1983), 7580.Google Scholar
Bognár, J.: An approach to the spectral decomposition of J-positizable operators, J. Operator Theory 17(1987), no. 2, 309326.Google Scholar
Bogachev, V. I.: Measure Theory, Springer-Verlag, Berlin 2007.Google Scholar
Bonsall, F. F. and Duncan, J.: Complete Normed Algebras, Springer-Verlag, Berlin 1973.Google Scholar
Bourbaki, N.: Topologie générale, ch. I, IX–X, Hermann, Paris 1961.Google Scholar
Bourbaki, N.: Intégration, ch. VII–VIII, Hermann, Paris 1961.Google Scholar
Bourbaki, N.: Topological Vector Spaces, Elements of Mathematics, ch. I–V, Springer-Verlag, Berlin 1987.Google Scholar
Carathéodory, C.: Über den Variabillitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann., 64(1907), 95115.CrossRefGoogle Scholar
Colojoară, I. and Foiaş, C.: Theory of Generalized Spectral Operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York 1968.Google Scholar
Constantinescu, T. and Gheondea, A.: Notes on (the Birmak-Krein-Vishik theory on) selfadjoint extensions of semibounded symmetric operators, in Two papers on selfadjoint extensions of symmetric semibounded operators, INCREST Preprint Series, July 1981, Bucharest, Romania, arXiv:1807.05363 [math.FA].Google Scholar
Constantinescu, T. and Gheondea, A.: On unitary dilation and characteristic functions in indefinite inner product spaces, in Operator Theory: Advances and Applications, Vol. 24, Birkhäuser, Basel 1987, pp. 87102.Google Scholar
Constantinescu, T. and Gheondea, A.: Extending factorizations and minimal negative signatures, J. Operator Theory, 28(1992), 371402.Google Scholar
Constantinescu, T. and Gheondea, A.: Elementary rotations of linear operators in Kreĭn spaces, J. Operator Theory, 29(1993), 167203.Google Scholar
Constantinescu, T. and Gheondea, A.: Representations of Hermitian kernels by means of Krein spaces, Publ. RIMS Kyoto Univ., 33(1997), 917951.Google Scholar
Constantinescu, T., Gheondea, A.: On a Nehari type problem on spaces with indefinite inner product, Rev. Roum. Math. Pures App. 43(1998), no. 3–4, 329354.Google Scholar
Cohn, D. L.: Measure Theory, Birkhäuser, New York 2013.Google Scholar
Conway, J. B.: Functions of One Complex Variable. I, 2nd edition, Springer-Verlag, Berlin 1978.Google Scholar
Conway, J. B.: A Course in Functional Analysis, Springer-Verlag, Berlin 1990.Google Scholar
Conway, J. B.: Functions of One Complex Variable. II, Springer-Verlag, Berlin 1995.Google Scholar
Conway, J. B.: A Course in Operator Theory, American Mathematical Society, Providence, RI 2000.Google Scholar
Ćurgus, B.: On the regularity of the critical point infinity of definitizable operators, Integral Equations Operator Theory, 8(1985), 462488.Google Scholar
Ćurgus, B., Gheondea, A., and Langer, H.: On singular critical points of positive operators in Krein spaces, Proc. Am. Math. Soc., 128(2000), 26212626.CrossRefGoogle Scholar
Ćurgus, B. and Langer, H.: Continuous embeddings, completions and complementation in Krein spaces, Rad. Mat., 12(2003), 3779.Google Scholar
Dieudonné, J.: Quasi-Hermitian operators, in Proc. Int. Symp. on Linear Spaces (Jerusalem, 1960), Jerusalem Academic Press, Jerusalem and Pergamon, Oxford 1961, pp. 115122.Google Scholar
Dijksma, A. and Gheondea, A.: Index formulae for subspaces of Kreĭn spaces, Integral Equations Operator Theory, 25(1996), no. 1, 5872.CrossRefGoogle Scholar
Dijksma, A., Langer, H., and de Snoo, H. S. V.: Unitary colligations in Kreĭn spaces and their role in the extension theory of isometric and symmetric linear relations in Hilbert spaces, in Functional Analysis II, Proceedings Dubrovnik 1985, Lecture Notes in Mathematics, Vol. 1242, Springer-Verlag, Berlin 1987, pp. 123143.Google Scholar
Dijksma, A., Langer, H., and de Snoo, H. S. V.: Representations of holomorphic operator functions by means of resolvents of unitary or selfadjoint operators in Kreĭn spaces, in Operators in Indefinite Metric Spaces, Scattering Theory and Other Topics, Birkhäuser, Basel 1987, pp. 123143.Google Scholar
Dixmier, J.: Les C*-algébres et leurs representations, Gauthier-Villars, Paris 1964.Google Scholar
Dixmier, J.: Les moyennes invariantes dans les semi-groupes et leurs applications, Acta Sci. Math. (Szeged), 12(1950), 213227.Google Scholar
Dritschel, M. A.: Extension Theorems for Operators in Kreĭn Spaces, Dissertation, University of Virginia 1989.Google Scholar
Dritschel, M. A.: A lifting theorem for bicontractions, J. Funct. Anal., 88(1990), 6189.Google Scholar
Dritschel, M. A.: The essential uniqueness property for linear operators on Kreĭn spaces, J. Funct. Anal., 118(1993), 198248.CrossRefGoogle Scholar
Dritschel, M. A.: A method for constructing invariant subspaces for some operators on Kreĭn spaces, in Operator Extensions, Interpolation of Functions and Related Topics, 14th International Conference on Operator Theory, Timişoara (Romania), June 1–5, 1992, Oper. Theory, Adv. Appl., Vol. 61, Birkhäuser, Basel 1993, pp. 85113.Google Scholar
Dritschel, M. A. and Rovnyak, J.: Extension theorems for contraction operators in Kreĭn spaces, in Operator Theory: Advances and Applications, Vol. 47, Birkhäuser Basel 1990, pp. 221305.Google Scholar
Dritschel, M. A. and Rovnyak, J.: Operators on indefinite inner product spaces, in Lectures on Operator Theory and Its Applications, Fields Institute Monographs, Vol. 3, American Mathematical Society, Providence, RI 1996, pp. 143232.Google Scholar
Dunford, N. and Schwartz, J. T.: Linear Operators. Part I. General Theory, Interscience, New York 1958.Google Scholar
Dunford, N. and Schwartz, J. T.: Linear Operators. Part II. Spectral Theory. Selfadjoint Operators in Hilbert Space, Interscience, New York 1963.Google Scholar
Fan, K.: Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Natl. Acad. Sci. USA, 38(1952), 121126.Google Scholar
Foiaş, C. and Frazho, A. E.: The Commutant Lifting Approach to Interpolation Problems, Birkhäuser, Basel 1990.Google Scholar
Gheondea, A.: On the geometry of pseudo-regular subspaces of a Kreĭn space, in Operator Theory: Advances and Applications, Vol. 14, Birkhäuser, Basel 1984, pp. 141156.Google Scholar
Gheondea, A.: Canonical forms of unbounded unitary operators in Kreĭn spaces, Publ. RIMS Kyoto Univ., 24(1988), 205224.CrossRefGoogle Scholar
Gheondea, A.: A geometric question concerning strong duality of neutral sub-spaces, Math. Balkanica, 3(1989), 183195.Google Scholar
Gheondea, A.: Quasi-contractions in Kreĭn spaces, in Operator Theory: Advances and Applications, Vol. 61, Birkhäuser, Basel 1993, pp. 123148.Google Scholar
Gheondea, A.: Contractive intertwining dilations of quasi-contractions, Z. Anal. Anwendungen, 15(1996), no. 1, 3144.Google Scholar
Gheondea, A.: On generalized interpolation and shift invariant maximal semidef-inite subspaces, in Operator Theory: Advances and Applications, Vol. 104, Birkhäuser, Basel 1998, pp. 121136.Google Scholar
Gheondea, A. and Jonas, P.: A characterization of spectral functions of definitizable operators, J. Operator Theory, 17(1987), 99110.Google Scholar
Ginuzburg, Yu. P.: On J-contractive operator functions [Russian], Dokl. Akad. Nauk. SSSR, 193(1970), 12181221.Google Scholar
Ginzburg, Yu. P.: Projections in a Hilbert space with a bilinear metric [Russian], Dokl. Akad. Nauk. SSSR, 139(1961), 775778; English translation Soviet Math. Dokl., 2(1961), 980-983.Google Scholar
Glicksberg, I. L., A further generalization of the Kakutani fixed theorem, with application to Nash equilibrium points, Proc. Am. Math. Soc., 3(1952) 170174.Google Scholar
Gohberg, I., Goldberg, S., and Kaashoek, M. A., Classes of Linear Operators, Vol. I, Springer, Basel 1990.Google Scholar
Gohberg, I., Goldberg, S., and Kaashoek, M. A., Classes of Linear Operators, Vol. II, Springer, Basel 1993.CrossRefGoogle Scholar
Gohberg, I., Lancaster, P., and Rodman, L.: Matrices in Indefinite Scalar Products, Birkhäuser, Basel 1983.Google Scholar
Greenleaf, F. P.: Invariant Means on Topological Groups and their Applications, Van Nostrand Reinhold, New York 1969.Google Scholar
Hara, T.: Operator inequalities and construction of Kreĭn space, Integral Equations Operator Theory, (1992), 551567.Google Scholar
Hansen, F.: Selfpolar norms on an indefinite inner product space, Publ. RISM Kyoto Univ., 16(1980), 401414.Google Scholar
Herglotz, G.: Über Pontezreihen mit positivem, reellem Teil im Eniheitskreis, Leipz. Ber., 63(1911), 501511.Google Scholar
Herglotz, G., Schur, I., Pick, G., Nevanlinna, R., Weyl, H.: Ausgewählte Arbeiten zu den Ursprängen der Schur-Analysis [Selected Works on the Origins of Schur Analysis] Gewidmet dem groß en Mathematiker Issai Schur (1875–1941) [Dedicated to the great mathematician Issai Schur (1875–1941)], Teubner-Archiv zur Mathematik [Teubner Archive on Mathematics], B. G. Teubner, Stuttgart 1991.Google Scholar
Iokhvidov, I. S.: On a lemma of Ky Fan generalizing the fixed-point principle of A.N. Tikhonov [Russian], Dokl. Akad. Nauk. SSSR, 159(1964), 501504.Google Scholar
Iokhvidov, I. S. and Kreĭn, M. G.: Spectral theory of operators in indefinite metric. I, Trud. Mosk. Mat. Obshch., 5(1956), 367432; English translation, Am. Math. Soc. Transl. (2), 13(1960), 105-175.Google Scholar
Iokhvidov, I. S. and Kreĭn, M. G.: Spectral theory of operators in indefinite metric. II, Trud. Mosk. Mat. Obshch., 9(1959), 413496; English translation, Am. Math. Soc. Transl. (2), 34(1963), 283–373.Google Scholar
Iokhvidov, I. S., Kreĭn, M. G., and Langer, H.: Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric, Akademie-Verlag, Berlin 1983.Google Scholar
Jonas, P.: Zur Existenz von Eigenspektralfunktionen mit Singulartitäten, Math. Nachr., 88(1977), 345361.Google Scholar
Jonas, P.: On the functional calculus and the spectral function for definitizable operators in Kreĭn space, Beitr. Anal., 16(1981), 121135.Google Scholar
Jonas, P.: On spectral distributions of definitizable operators in Kreĭnspace, in Spectral Theory, Vol. 8 of Banach Center Publications, PWN Polish Scientific Publishers, Warsaw 1982.Google Scholar
Jonas, P.: On locally definite operators in Krein spaces, Spectral Analysis and its Applications, Theta Ser. Adv. Math., 2, Theta, Bucharest 2003, pp. 95127.Google Scholar
Kato, T.: Perturbation Theory of Linear Operators, Springer-Verlag, Berlin 1966.Google Scholar
Kaltenbäck, M.: Spectral theorem for definitizable normal linear operators on Krein spaces, Integral Equations Operator Theory, 85(2016), 221243.Google Scholar
Kaltenbäck, M.: Definitizability of normal operators on Krein spaces and their functional calculus, Integral Equations Operator Theory, 87(2017), 461490.Google Scholar
Kaltenbäck, M. and Skrepek, N.: Joint functional calculus for definitizable self-adjoint operators on Krein spaces, Integral Equations Operator Theory, 92(2020), no. 4, Paper no. 29, 36 p.CrossRefGoogle Scholar
Kelley, J. L.: General Topology, Springer-Verlag, Berlin 1955.Google Scholar
Knaster, B., Kuratowski, C., and Mazurkiewicz, S.: Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe, Fund. Math., 14(1929), 132137.Google Scholar
Koosis, P.: Introduction to Hp Theory, London Math. Soc. Lecture Note Ser., Vol. 40, Cambridge University Press, New York 1980.Google Scholar
Kreĭn, M. G.: Completely continuous linear operators in function spaces with two norms [Ukrainian], Akad. Nauk Ukrain. RSR Zbirnik Prac. Inst. Mat., 9(1947), 104129.Google Scholar
Kreĭn, M. G.: The theory of selfadjoint extensions of semibounded Hermitian transformations and its applications. I [Russian], Mat. Sbornik 20(1947), 431495.Google Scholar
Kreĭn, M. G.: Introduction to the geometry of indefinite inner product J-spaces and to the theory of operators in those spaces, in Second Math. Summer School [Russian], part I, Naukova Dumka, Kiev, 1965, pp. 1592; English translation, Am. Math. Soc. Transl., (2) 93 (1970), 103–176.Google Scholar
Kreĭn, M. G. and Langer, H.: On the spectral function of selfadjoint operators in spaces with indefinite metric [Russian], Dokl. Akad. Nauk, 152(1963), 3942.Google Scholar
Kreĭn, M. G. and Langer, H.: Über die veralgemeinerte Resolventen und die characteristische Funktion eines isometrischen Operators im Raume Πκ, In: Colloquia Math. Soc. János Bolyai, Vol. 5, Hilbert Space Operators and Operator Algebras, North-Holland, Amsterdam 1972, pp. 353399.Google Scholar
Kreĭn, M. G. and Langer, H.: Über einige Fortsetzunsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen, Math. Nachr., 77(1977), 187236.CrossRefGoogle Scholar
Kreĭn, M. G. and Langer, H.: Über einige Fortsetzunsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zusammenhangen. II. Veralgemeinerte Resolventen u-Resolventen und ganze Operatoren, J. Funct. Anal., 30(1978), 390147.Google Scholar
Kreĭn, M. G. and Langer, H.: On some extension problems which are closely connected with the theory of Hermitian operators in a space Πκ. III. Indefinite analogues of the Hamburger and Stieltjes moment problem, Beitr. Anal., Part (I), 14(1979), 2540; Part (II), 15(1981), 27-45.Google Scholar
Kreĭn, M. G. and Langer, H.: On some propositions on analytic matrix functions related to the theory of operators in the spaces Πκ, Acta Sci. Math. (Szeged), 43(1981), 181205.Google Scholar
Kreĭn, M. G. and Shmulyan, Yu. L.: Plus-operators in a space with an indefinite metric [Russian], Mat. Issled., 1(1966), 131161.Google Scholar
Kreĭn, M. G. and Shmulyan, Yu. L.: J-Polar representations of plus-operators [Russian], Mat. Issled., 1(1966), 172210.Google Scholar
Kreĭn, M. G. and Shmulyan, Yu. L.: On a class of operators in a space with an indefinite metric [Russian], Dokl. Akad. Nauk USSR, 170(1966), 3437.Google Scholar
Kreĭn, M. G. and Shmulyan, Yu. L.: Linear fractional transformations with operator coefficients [Russian], Mat. Issled., 2(1967), 6496.Google Scholar
Langer, H.: Spektraltheorie linearer Operatoren in J-Räumen und einige Anwendungen auf den Schar L(λ) = λ2 + λB + C, Habilitationsschrift, Dresden 1965.Google Scholar
Langer, H.: Invariante Teilräume definisierbarer J-selbstajungierter Operatoren, Ann. Acad. Sci. Fenn. Ser. A I, 475(1971).Google Scholar
Langer, H.: Spectral functions of definitizable operators in Kreĭn spaces, in Functional Analysis, Proceedings, Dubrovnik 1981, Lecture Notes in Mathematics Vol. 948, Springer-Verlag, Berlin 1982, pp. 116.Google Scholar
Langer, H., Markus, A., and Matsaev, V.: Locally definite operators in indefinite inner product spaces, Math. Ann., 308(1997), 405424.Google Scholar
Lax, P. D.: Symmetrizable linear transformations, Commun. Pure. Appl. Math., 7(1954), 633647.Google Scholar
Lax, P. D.: Translation invariant spaces, Acta Math., 101(1959), 163178.Google Scholar
Nehari, Z.: On bounded bilinear forms, Ann. Math., 65(1957), 153162.Google Scholar
Nevanlinna, R.: Sur un probléme d’interpolation, C. R. Acad. Sci. Paris 188(1929), 12241226.Google Scholar
Nevanlinna, R.: Erweiterung der Theorie des Hilbertschen Raumes, Comm. Sem. Math. Univ. Lund., Tome Supplementaire, (1952), 160168.Google Scholar
Nevanlinna, R.: Über metrische lineare Räume. II. Bilineareformen und Stetigkeit. Ann. Acad. Sci. Fenn. Ser. A I, 113(1952).Google Scholar
Nevanlinna, R.: Über metrische lineare Räume. III. Theorie der Orhogonalsys-teme. Ann. Acad. Sei. Fenn. Ser. A I, 115(1952).Google Scholar
Nevanlinna, R.: Über metrische lineare Räume. IV. Zur Theorie der Unter-räume. Ann. Acad. Sci. Fenn. Ser. A I, 163(1952).Google Scholar
Pedersen, G.: Analysis Now, Springer-Verlag, Berlin 1989.Google Scholar
Pick, G.: Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt werden, Math. Ann., 77(1916), 723.Google Scholar
Phillips, R. S.: Dissipative operators and parabolic partial differentioal equations, Commun. Pure Appl. Math., 12(1959), 249276.Google Scholar
Phillips, R. S.: Dissipative operators and hyperbolic systems of partial differential equations, Trans. Am. Math. Soc., 90(1959), 193254.Google Scholar
Phillips, R. S.: The extension of dual subspaces invariant under and algebra, on Proc. Int. Symp. Linear Spaces, Jerusalem Academic Press, Jerusalem and Pergamon, Oxford 1961, pp. 366398.Google Scholar
Pontryagin, L. S.: Hermitian operators in spaces with indefinite metric [Russian], Izv. Akad. Nauk. SSSR Ser. Mat., 8(1944), 243236.Google Scholar
Potapov, V. P.: The multiplicative structure of J-contractive analytic matrix functions [Russian], Trudy Mosk. Mat. Obshch., 4(1955), 125236; English translation, Am. Math. Soc. Transl. (2), 15(1960), 131-243.Google Scholar
Power, S. C.: Hankel Operators on Hilbert Space, Pitman, Boston, MA 1982.Google Scholar
Reid, W. T.: Symmetrizable completely continuous linear transformations in Hilbert space, Duke Math. J., 18(1951), 4156.Google Scholar
Rickart, C. E.: General Theory of Banach Algebras, Van Nostrand, Princeton, NJ 1960.Google Scholar
Rosenblum, M. and Rovnyak, J.: Hardy Classes and Operator Theory, Oxford Math. Monographs, Oxford University Press, New York 1985.Google Scholar
Rudin, W.: Real and Complex Analysis, McGraw-Hill, Singapore 1987.Google Scholar
Rudin, W.: Functional Analysis, 2nd edition, Springer-Verlag, Berlin 1991.Google Scholar
Ryan, R. A.: Introduction to Tensor Products of Banach Spaces, Springer-Verlag, London 2002.CrossRefGoogle Scholar
Sarason, D.: Generalized interpolation in H, Trans. Am. Math. Soc. , 127(1967), 179203.Google Scholar
Schaefer, H. H.: Topological Vector Spaces, Springer-Verlag, Berlin 1970.Google Scholar
Schmüdgen, K.: Unbounded Self-adjoint Operators on Hilbert Space, Springer, Dordrecht 2012.Google Scholar
Schur, I.: Über Pontezreihen, die im Innern des Einheitskreises beschränkt sind, J. Reine Angew. Math., 117(1917), 205232.Google Scholar
Schwartz, L.: Sous espaces Hilbertiens d’espace vectoriel topologiques et noyaux associés (noyaux reproduisants), J. Anal. Math., 13(1973), 115256.Google Scholar
Shmulyan, Yu. L.: Theory of linear relations and spaces with indefinite metric [Russian], Funkts. Anal. Pril. 10(1976).Google Scholar
Sobolev, S. L.: The motion of a symmetric top cavity filled with a liquid [Russian], Ž. Prikl. Meh. i Tehn. Fiz., 3(1960), 2055.Google Scholar
Stieltjes, T. J.: Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 8(1894), 122.Google Scholar
Strauss, V.: Models of function type for commutative symmetric operator families in Krein spaces, Abstr. Appl. Anal., 2008, Article ID 439781, 40 p.Google Scholar
Sz, B..-Nagy: On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math., 11(1947), 152157.Google Scholar
Nagy, B. Sz.- and Foiaş, C.: Commutants de certains opérateurs, Acta. Math. (Szeged), 29(1968), 117.Google Scholar
Nagy, B. Sz.- and Foiaş, C.: Harmonic Analysis of Operators on Hilbert Space, North-Holland, New York 1970.Google Scholar
Tomita, M.: Operators and operator algebras in Kreĭn spaces, RIMS Kokiuuroku, 398(1980), 131158.Google Scholar
Treil, S. and Volberg, A.: A fixed point approach to Nehari’s problem and its applications, in Operator Theory: Advances and Applications, Vol. 71, Birkhäuser, Basel 1994, pp. 165186.Google Scholar
Young, N. J.: Orbits of the unit sphere of L(H, K) under symplectic transformations, J. Operator Theory, 11(1984), 171191.Google Scholar
Young, N. J.: J-Unitary equivalence of positive subspaces of a Kreĭn space, Acta Sci. Math. (Szeged), 47(1984), 107111.Google Scholar

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  • References
  • Aurelian Gheondea, Bilkent University, Ankara
  • Book: An Indefinite Excursion in Operator Theory
  • Online publication: 08 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108979061.016
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  • References
  • Aurelian Gheondea, Bilkent University, Ankara
  • Book: An Indefinite Excursion in Operator Theory
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  • Chapter DOI: https://doi.org/10.1017/9781108979061.016
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  • References
  • Aurelian Gheondea, Bilkent University, Ankara
  • Book: An Indefinite Excursion in Operator Theory
  • Online publication: 08 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108979061.016
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