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On generalized semi B-Fredholm operators

Abstract:

In this paper we study two new classes of bounded linear operators acting on a Banach space X called lower semi B-Fredholm generalized operators and lower semi Saphar operators, respectively. We characterize a generalized semi B-Fredholm operator as the direct sum of a nilpotent operator and a semi Shapar operator and also we prove the stability of this class of operators under perturbations by operators with finite-range power.