Some properties of (m;C)-isometric operators

Abstract

In this paper, we study if T is an (m;C)-isometric operator and CTC commutes with T, then T is an (m;C)-isometric operator. we also study local spectral properties and spectral relations of (m;C)-isometric operators, such as property (), decomposability, the single-valued extension property and Dunford’s boundedness. We also study perturbation of (m;C)-isometric operators by nilpotent operators and by algebraic operators and give some properties.