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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$.

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

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Keywords: Von Neumann's inequality, Pick-Nevanlinna theorem
Article copyright: © Copyright 1982 American Mathematical Society