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Proceedings of the American Mathematical Society

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A generalization of von Neumann's inequality to the complex ball


Author: S. W. Drury
Journal: Proc. Amer. Math. Soc. 68 (1978), 300-304
MSC: Primary 47A30
DOI: https://doi.org/10.1090/S0002-9939-1978-0480362-8
MathSciNet review: 480362
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Abstract | References | Similar Articles | Additional Information

Abstract: A necessary and sufficient condition is found for a polynomial Q of J variables to be such that $ Q({A_1}, \ldots ,{A_J})$ is a contraction whenever $ {A_j}(1 \leqslant j \leqslant J)$ are commuting linear operators on complex hilbert space satisfying $ \Sigma _{j = 1}^JA_j^ \ast {A_j} \leqslant I$.


References [Enhancements On Off] (What's this?)

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  • [2] M. J. Crabb and A. M. Davie, Von Neumann's inequality for Hilbert space operators, Bull. London Math. Soc. 7 (1975), 49-50. MR 0365179 (51:1432)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0480362-8
Keywords: Functional calculus, operators on hilbert space
Article copyright: © Copyright 1978 American Mathematical Society

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