Lipschitz Operators and Hölder-Zygmund Functions with Estimates of Operator Moduli of Continuity

Abstract

We classify the functional model for dissipative and calculus for a pair of almost commuting selfadjoint operators. We find the estimates in operator class for a difference of function from the pick class of accretive operators and of operator moduli of continuity .We discuss the Hankel operators in the perturbation theory for unitary, selfadjoint operators, functions of perturbed and normal operators .We show an extension of the koplienko - Neidhardt trace formule and the differential properties of some dense subalgebras of C*-algebras with multiple operator integrals and higher operator derivatives. We determine the fully operator Lipschitz and Hölder–Zygmund functions .