Dissipative operators and operator Lipschitz functions

TL;DR

This paper develops an integral representation for differences of functions of maximal dissipative operators, enabling Lipschitz estimates and analysis of quasicommutators, advancing operator theory in dissipative contexts.

Contribution

It introduces a novel integral representation for differences of functions of maximal dissipative operators, facilitating Lipschitz estimates and quasicommutator analysis.

Findings

Established integral representation for operator differences

Derived Lipschitz type estimates for dissipative operators

Analyzed quasicommutators in the dissipative operator setting

Abstract

The purpose of this paper is to obtain an integral representation for the difference $f(L_1)-f(L_2)$ of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish Lipschitz type estimates for functions of maximal dissipative operators. We also consider a similar problem for quasicommutators, i.e., operators of the form $f(L_1)R-Rf(L_2)$.