Geodesic
Perturbations of operators similar to contractions and the commutator equation
C. Badea1
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
@article{10_4064_sm150_3_5,
     author = {C. Badea},
     title = {Perturbations of operators similar to contractions
and the commutator equation},
     journal = {Studia Mathematica},
     pages = {273--293},
     publisher = {mathdoc},
     volume = {150},
     number = {3},
     year = {2002},
     doi = {10.4064/sm150-3-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm150-3-5/}
}
TY  - JOUR
AU  - C. Badea
TI  - Perturbations of operators similar to contractions
and the commutator equation
JO  - Studia Mathematica
PY  - 2002
SP  - 273
EP  - 293
VL  - 150
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm150-3-5/
DO  - 10.4064/sm150-3-5
LA  - en
ID  - 10_4064_sm150_3_5
ER  - 
%0 Journal Article
%A C. Badea
%T Perturbations of operators similar to contractions
and the commutator equation
%J Studia Mathematica
%D 2002
%P 273-293
%V 150
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm150-3-5/
%R 10.4064/sm150-3-5
%G en
%F 10_4064_sm150_3_5
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

Cité par Sources :