Essential spectrum of upper triangular operator matrices

Abstract

This paper is concerned with general $$n\times n$$ upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their left (right) essential spectrum and essential spectrum are given, based on the space decomposition technique. Moreover, some sufficient and necessary conditions are given under which the left (right) essential spectrum and the essential spectrum of such operator matrix, respectively, coincide with the union of the left (right) essential spectrum and the essential spectrum of its diagonal entries.