On the Kato, semi-regular and essentially semi-regular spectra

Abstract

In this paper, we give some proprieties  of the  semi-regular, essentially semi-regular and the operators of Kato type   on a Banach space. We also show that the essentially semi-regular spectrum of closed, densely defined linear operator is stable under commuting compact perturbation and  its  Kato  spectrum  is stable subjected to additive commuting nilpotent perturbations.