Perturbations of Operators Similar to Contractions and the Commutator Equation
نویسنده
چکیده
Abstract. 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 ) (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 .
منابع مشابه
On a functional equation for symmetric linear operators on $C^{*}$ algebras
Let $A$ be a $C^{*}$ algebra, $T: Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $. We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: i) $A$ is a simple $C^{*}$-algebra. ii) $A$ is unital with trivial center and has a faithful trace such ...
متن کاملLimiting absorption principle for some long range perturbations of Dirac systems at threshold energies
We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of non-self-adjoint operators. The technique is based on a positive commutator theory for non self-adjoint operators, which we develop in appendix. We also discuss so...
متن کاملp-SUMMABLE COMMUTATORS IN DIMENSION d
We show that many invariant subspaces M for d-shifts (S1, . . . , Sd) of finite rank have the property that the orthogonal projection PM onto M satisfies PMSk − SkPM ∈ L, 1 ≤ k ≤ d for every p > 2d, L denoting the Schatten-von Neumann class of all compact operators having p-summable singular value lists. In such cases, the d tuple of operators T̄ = (T1, . . . , Td) obtained by compressing (S1, ....
متن کاملSelf-commutators of composition operators with monomial symbols on the Bergman space
Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...
متن کاملCommutator Estimate for Nonlinear Subdivision
Nonlinear multiscale algorithms often involve nonlinear perturbations of linear coarse-to-fine prediction operators S (also called subdivision operators). In order to control these perturbations, estimates of the “commutator” SF − FS of S with a sufficiently smooth map F are needed. Such estimates in terms of bounds on higher-order differences of the underlying mesh sequences have already appea...
متن کامل