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Perturbations of operators similar to contractions and the commutator equation | Catalin Badea
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11 Dec 2004 | Journal: | Studia Math. 150(2002), 273-293 | Subject: | Functional Analysis MSC-class: 47A50 | math.FA | Abstract: | Let $T$ 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 | Services: | Forum | Review | PDF | Favorites |
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