A converse to von Neumann’s inequality
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- by James Rovnyak PDF
- Proc. Amer. Math. Soc. 84 (1982), 370-372 Request permission
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 $\left \| {{f_0}(T)} \right \| \leqslant 1$ for every contraction operator $T$ on a Hilbert space whose spectrum is contained in $G$, then ${f_0} = f|G$ where $f$ is holomorphic and bounded by 1 on $D$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 370-372
- MSC: Primary 47A60; Secondary 30A10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640233-1
- MathSciNet review: 640233