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

Abstract

In this paper, we give some properties 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.