Characteristic Functions of Joint Invariant Subspaces and Perturbation of Normal Operators with Enlargements of Minimal Volume

Abstract

We show the operators with singular continuous spectrum : ranke one operators and perturbations, Hausdorff dimensions and localization. We study the rank one perturbations of self-adjoint, diagonal and normal operators with generalization of projection constants. Minimal volume shadows and projections of cubes and totally unimodular matrices are considered. We discuss the characteristic functions for infinite sequences of non-commuting operators and joint invariant subspaces. We show the sufficient enlargements of minimal volume for projections and infinite dimensional normed linear spaces.