Perturbations of operators similar to contractions and the commutator equation
Badea, Catalin
HAL, hal-00012447 / Harvested from HAL
Text on HAL
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 $R(0;T,V)=T\\oplus V$.
Publié le : 2002-07-05
Classification:  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 
@article{hal-00012447,
     author = {Badea, Catalin},
     title = {Perturbations of operators similar to contractions and the commutator equation},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00012447}
}

Badea, Catalin. Perturbations of operators similar to contractions and the commutator equation. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00012447/