On some functional calculus of closed operators on Banach space. III. Some topics of perturbation theory

This work is a continuation of research of A.A. Atvinovskii and the author of functional calculus of closed operators on Banach spaces based on Markov and related functions as symbols. The following topics in the perturbation theory are considered: estimates of bounded perturbations of operator functions with respect to general operator ideal norms, operator Lipschitzness, moment inequality, Freshet operator differentiability, analyticity of operator functions under consideration with respect to the perturbation parameter, spectral shift function and Livshits–Krein trace formula.