Perturbations of operators similar to contractions and the commutator equation

Badea, Catalin

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Perturbations of operators similar to contractions and the commutator equation

Author(s) :

Badea, Catalin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Studia Mathematica

Pages :

273-293

Publisher :

Instytut Matematyczny - Polska Akademii Nauk

Publication date :

2002

ISSN :

0039-3223

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

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 ...
Show more >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 $R(0;T,V)=T\\oplus V$.Show less >

Language :

Anglais

Popular science :

Non

Comment :

26 pages, Preprint version

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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