Perturbations of operators similar to contractions and the commutator equation

Details Perturbations of operators similar to contractions and the commutator equation Perturbations of operators similar to contractions and the commutator equation

2005-01-11

arxiv.org/abs/math/0501154v1

Studia Math. 150(2002), 273-293

Mathematics

Functional Analysis

26 pages, Preprint version

Scientific paper

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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