Geodesic
Perturbations of operators similar to contractions and the commutator equation
C. Badea 1
1 Département de Mathématiques UMR 8524 au CNRS Université de Lille 1 F-59655 Villeneuve d'Ascq, France
Studia Mathematica, Tome 150 (2002) no. 3, pp. 273-293 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $T$ and $V$ be two Hilbert space contractions and let $X$ be a linear bounded operator. It was proved by C. Foiaş and J. P. Williams that in certain cases the operator block matrix $R(X;T,V)$ (equation (1.1) below) 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 $R(0;T,V)=T\oplus V$.
DOI : 10.4064/sm150-3-5
Keywords: hilbert space contractions linear bounded operator proved foia williams certain cases operator block matrix v equation below similar contraction only commutator equation tz zv has bounded solution characterize here similarity contractions operator matrices v terms growth conditions perturbations oplus

C. Badea  1

1 Département de Mathématiques UMR 8524 au CNRS Université de Lille 1 F-59655 Villeneuve d'Ascq, France 
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C. Badea. Perturbations of operators similar to contractions
and the commutator equation. Studia Mathematica, Tome 150 (2002) no. 3, pp. 273-293. doi: 10.4064/sm150-3-5

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