Functions of perturbed pairs of noncommutative dissipative operators

Author:

Aleksandrov A.,Peller V.

Abstract

Let a function f f belong to the inhomogeneous analytic Besov space ( B , 1 1 ) + ( R 2 ) (B_{\infty ,1}^{\,1})_+(\mathbb {R}^2) . For a pair ( L , M ) (L,M) of not necessarily commuting maximal dissipative operators, the function f ( L , M ) f(L,M) of L L and M M is defined as a densely defined linear operator. For p [ 1 , 2 ] p\in [1,2] , it is proved that if ( L 1 , M 1 ) (L_1,M_1) and ( L 2 , M 2 ) (L_2,M_2) are pairs of not necessarily commuting maximal dissipative operators such that both differences L 1 L 2 L_1-L_2 and M 1 M 2 M_1-M_2 belong to the Schatten–von Neumann class S p {\boldsymbol S}_p , then for an arbitrary function f f in (\mathcyr {B}_{\infty ,1}^{\,1})_+(\mathbb {R}^2), the operator difference f ( L 1 , M 1 ) f ( L 2 , M 2 ) f(L_1,M_1)-f(L_2,M_2) belongs to S p {\boldsymbol S}_p and the following Lipschitz type estimate holds: \begin{equation*} \|f(L_1,M_1)-f(L_2,M_2)\|_{{\boldsymbol S}_p} \le const\|f\|_{\mathcyr {B}_{\infty ,1}^{\,1}}\max \big \{\|L_1-L_2\|_{{\boldsymbol S}_p},\|M_1-M_2\|_{{\boldsymbol S}_p}\big \}. \end{equation*}

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Reference16 articles.

1. Functions of noncommuting self-adjoint operators under perturbation and estimates of triple operator integrals;Aleksandrov, A. B.;Adv. Math.,2016

2. Functions of perturbed dissipative operators;Aleksandrov, A. B.;Algebra i Analiz,2011

3. Operator Lipschitz functions;Aleksandrov, A. B.;Uspekhi Mat. Nauk,2016

4. Multiple operator integrals, Haagerup and Haagerup-like tensor products, and operator ideals;Aleksandrov, A. B.;Bull. Lond. Math. Soc.,2017

5. Dissipative operators and operator Lipschitz functions;Aleksandrov, A. B.;Proc. Amer. Math. Soc.,2019

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