Relationship between a variant of essential spectrum and the Kato essential spectrum

Abstract

JP Labrousse [8] studied and characterized in the case of Hilbert spaces, a relation between the Kato essential spectrum (essential quasi-Fredholm spectrum) and another essential spectrum defined by σec (T)= 1λ∈ C; R (λI-T) is not closedl (see [3]). In this paper, we investigate this relation in the case of Banach spaces.