%0 Journal Article
%T Perturbations of operators similar to contractions and the commutator equation
%A Catalin Badea
%J Mathematics
%D 2005
%I arXiv
%X 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 $R(0;T,V)=T\oplus V$.
%U http://arxiv.org/abs/math/0501154v1