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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-3-5,
author = {C. Badea},
title = {Perturbations of operators similar to contractions and the commutator equation},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {273-293},
zbl = {1015.47011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-3-5}
}
C. Badea. Perturbations of operators similar to contractions and the commutator equation. Studia Mathematica, Tome 151 (2002) pp. 273-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-3-5/