Relationship between the essential quasi-Fredholm spectrum and the closed-range spectrum, An

Abstract

J. P. Labrousse [13] studied and characterized in the case of Hilbert spaces, a relation of the essential quasi-Fredholm spectrum and the spectrum de ned by Goldberg in [9] by ec(A) = f 2 C ; R( I 􀀀 A) is not closedg. In this paper, we investigate this relation in the case of Banach spaces. A similar relation is given, if we consider a B-Fredholm spectrum instead of the essential quasi-Fredholm spectrum.