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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A converse to von Neumann's inequality


Author: James Rovnyak
Journal: Proc. Amer. Math. Soc. 84 (1982), 370-372
MSC: Primary 47A60; Secondary 30A10
MathSciNet review: 640233
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Abstract: The Pick-Nevanlinna theorem is used to show that if $ {f_0}$ is holomorphic on an open subset $ G$ of the unit disk $ D$ and $ \left\Vert {{f_0}(T)} \right\Vert \leqslant 1$ for every contraction operator $ T$ on a Hilbert space whose spectrum is contained in $ G$, then $ {f_0} = f\vert G$ where $ f$ is holomorphic and bounded by 1 on $ D$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0640233-1
PII: S 0002-9939(1982)0640233-1
Keywords: Von Neumann's inequality, Pick-Nevanlinna theorem
Article copyright: © Copyright 1982 American Mathematical Society