Perturbations of operators similar to contractions and the commutator equation

• Autorzy: C. Badea
• Języki publikacji: EN

Abstrakty

EN

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 ⊕ V.

Kategorie tematyczne

• 47A55: Perturbation theory
• 47A50: Equations and inequalities involving linear operators, with vector unknowns
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 150
• Numer: 3
• Strony: 273-293

Daty

wydano

2002

Twórcy

autor

C. Badea

• Département de Mathématiques, UMR 8524 au CNRS, Université de Lille 1, F-59655 Villeneuve d'Ascq, France

Identyfikatory

DOI

10.4064/sm150-3-5