  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.
