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Polarization and the two-dimensional Grothendieck inequality

Published online by Cambridge University Press:  24 October 2008

Andrew Tonge
Affiliation:
Department of Mathematics and Statistics, Brunel University

Extract

Throughout this paper all scalars and vector spaces will be assumed to be complex unless there are specific indications to the contrary.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Beckenbach, E. F. and Bellman, R.. Inequalities. Springer (Ergebnisse der Math. Band 30), Berlin, 1971.Google Scholar
[2]Davie, A. M.. Quotient algebras of uniform algebras. J. London Math. Soc. (2) 7 (1973), 3140.Google Scholar
[3]Davie, A. M.. Power bounded elements in a Q-algebra. Bull. London Math. Soc. 6 (1974), 6165.Google Scholar
[4]Dineen, S.. Complex Analysis in Locally Convex Spaces. North Holland Mathematics Studies, vol. 57 (1981).Google Scholar
[5]Drury, S. W.. Remarks on Von Neumann's Inequality. In Banach Spaces, Harmonic Analysis and Probability Theory, Lecture Notes in Mathematics vol. 995 (Springer-Verlag, 1983), 1432.Google Scholar
[6]Fournier, J. J. F.. Multilinear Grothendieck inequalities via the Schur algorithm. Canad. Math. Soc. Conference Proc. vol. 1.Google Scholar
[7]Grothendieck, A.. Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8 (1956), 179.Google Scholar
[8]Harris, L.. Bounds on the derivatives of holomorphic functions of vectors. Colloque d'analyse, Rio de Janeiro, 1972 (ed. Nachbin, L.), Actualités Sci. Ind. no. 1367 (Hermann, 1975), 145163.Google Scholar
[9]Krivine, J. L.. Constantes de Grothendieck et fonctions de type positif sur les sphéres. Adv. in Math. 31 (1979), 1630.Google Scholar
[10]Lindenstrauss, J. and Tzafriri, L.. Classical Banach Spaces I. Ergebnisse der Math., Band 92, (Springer, 1977).Google Scholar
[11]Peller, V. V.. Estimates of functions of power bounded operators on Hilbert spaces. J. Operator Theory 7 (1982), 341372.Google Scholar
[12]Pisier, G.. Grothendieck's theorem for non-commutative C*-algebras with an appendix on Grothendieck's constants. J. Funct. Anal. 29 (1978), 397415.Google Scholar
[13]Tonge, A. M.. The von Neumann inequality for polynomials in several Hilbert–Schmidt operators. J. London Math. Soc. 2 18 (1978), 519526.Google Scholar
[14]Tonge, A. M.. Low dimensional Grothendieck constants. Brunei University Technical Report (1983).Google Scholar
[15]Varopoulos, N. Th.. On an inequality of von Neumann and an application of the metric theory of tensor products to operator theory. J. Funct. Anal. 16 (1974), 83100.Google Scholar
[16]Varopoulos, N. Th.. On a commuting family of contractions on a Hilbert space. Rev. Roumaine Math. Pures Appl. 21 (1976), 12831285.Google Scholar