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Perturbations of operators similar to contractions and the commutator equation

Catalin Badea
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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 $R(0;T,V)=T\oplus V$.

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Catalin Badea. 2005-01-11. Perturbations of operators similar to contractions and the commutator equation. https://arxiv.org/abs/math/0501154

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