ON ALGEBRAIC AND ANALYTIC CORE II

Abstract

In this paper, we continue the study of the algebraic core spectrum and the analytic core spectrum of an operator T on the complex Banach space X: σ_alc(T) = {λ ∈ \(\mathbb{C}\) : C(λI− T ) = {0}} and σ_ac(T) = {λ ∈ \(\mathbb{C}\) : K(λI− T ) = {0}} where C(T) and K(T) are respectively the algebraic core and the analytic core for T.  We shall be concerned with the relations between σ_ac(·) (σ_alc(·)) and different classical parts of spectrum: the point spectrum, the approximate point spectrum, the surjectivity spectrum and the Kato spectrum.  Moreover, some applications are given.