Some topics in the perturbation theory for a functional calculus of closed operators on Banach spaces

TL;DR

This paper advances the functional calculus for closed operators on Banach spaces, providing new estimates and properties related to perturbations, Lipschitzness, differentiability, and trace formulas.

Contribution

It introduces new results on perturbation estimates, operator Lipschitzness, and trace formulas within a specialized functional calculus framework for Banach space operators.

Findings

Derived bounds for bounded perturbations using operator ideal norms

Established conditions for operator Lipschitzness and differentiability

Extended Livshitz-Krein trace formulae to new classes of operators

Abstract

The wark is a contribution to the functional calculus constructed by of the author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus is based on Markov and related functions as symbols. Estimates of bounded perturbations of operator functions with respect to general operator ideal norms, operator Lipschitzness, moment inequality, Freshet operator differentiability, and Livshitz-Krein trace formulae have been considered.