Function of Perturbed Tuples of Selfadjoint Operators and the Locally Normal Operators in Krein Spaces

Abstract

We give the structure of the selfadjoint analytic operator functions and in 􀜵 -spaces. We also give the characterizations of the spectral functions of products of selfadjoint operators and on a class of 􀜬-selfadjoint operators with empty resolvent set. We show the Lipschitz functions of perturbed and finite rank perturbations of operators and definitizable operators. Functions of perturbed normal and tuples of selfadjoint and normal operators are studied. Operators, frames, local spectral for definite normal operators in Krein spaces are considered.