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29 March 2024
 
  » arxiv » math.FA/0501154

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Perturbations of operators similar to contractions and the commutator equation
Catalin Badea ;
Date 11 Dec 2004
Journal Studia Math. 150(2002), 273-293
Subject Functional Analysis MSC-class: 47A50 | math.FA
AbstractLet $T$ and $V$ be two Hilbert space contractions and let $X$ be a linear bounded operator. It was proved by C. Foias and J.P. Williams that in certain cases the operator block matrix $R(X;T,V)$ (defined in the text) is similar to a contraction if and only if the commutator equation $X = TZ-ZV$ has a bounded solution $Z$. We characterize here the similarity to contractions of some operator matrices $R(X;T,V)$ in terms of growth conditions or of perturbations of $R(0;T,V)=Toplus V$.
Source arXiv, math.FA/0501154
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