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Contractions without cyclic vectors

Authors: Béla Sz.-Nagy and Ciprian Foiaş
Journal: Proc. Amer. Math. Soc. 87 (1983), 671-674
MSC: Primary 47A15; Secondary 47A20
MathSciNet review: 687638
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Abstract: It is proved that if $ T$ is a completely nonunitary contraction on Hilbert space such that $ {T^{*n}}$ does not converge strongly to 0 as $ n \to \infty $, there is an integer $ N > 0$ so that none of the powers $ {T^{*m}}$ with $ m \geqslant N$ has a cyclic vector. Both conditions on $ T$ are essential, and the integer $ N$ is not universal, i.e., it depends on $ T$.

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

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Keywords: Contraction, cyclic vector, unitary and isometric dilation
Article copyright: © Copyright 1983 American Mathematical Society

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