Perturbations of operators similar to contractions and the commutator equation

@article{C2002,
abstract = {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.},
author = {C. Badea},
journal = {Studia Mathematica},
keywords = {contractions; commutator equation; similarity to contractions; operator perturbation; isometry; coisometry; unilateral shift},
language = {eng},
number = {3},
pages = {273-293},
title = {Perturbations of operators similar to contractions and the commutator equation},
url = {http://eudml.org/doc/285020},
volume = {150},
year = {2002},
}

TY - JOUR
AU - C. Badea
TI - Perturbations of operators similar to contractions and the commutator equation
JO - Studia Mathematica
PY - 2002
VL - 150
IS - 3
SP - 273
EP - 293
AB - 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.
LA - eng
KW - contractions; commutator equation; similarity to contractions; operator perturbation; isometry; coisometry; unilateral shift
UR - http://eudml.org/doc/285020
ER -