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Zapiski Nauchnykh Seminarov LOMI, 1987, Volume 157, Pages 165–172
(Mi znsl5215)
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Short communications
Some analogues of von-Heumann's inequality for $J$-contractions
M. M. Malamud
Abstract:
Let $J$ be a self-adjoint operator satisfying $J^2=I$. We prove that for any $J$-contraction $T$ (i. e. $T^*JT-J\leqslant0$) and any inner function $f$ holomorphic on the spectrum of $T$ the function $f(T)$ is a $J$-contraction too. It is also proved that for $J\ne\pm I$ only inner functions $f$ satisfy this property. We consider other analogues of von-Neumann's inequality.
Citation:
M. M. Malamud, “Some analogues of von-Heumann's inequality for $J$-contractions”, Investigations on linear operators and function theory. Part XVI, Zap. Nauchn. Sem. LOMI, 157, "Nauka", Leningrad. Otdel., Leningrad, 1987, 165–172
Linking options:
https://www.mathnet.ru/eng/znsl5215 https://www.mathnet.ru/eng/znsl/v157/p165
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Abstract page: | 115 | Full-text PDF : | 54 |
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