On Left and Right Semi-B-Fredholm Operators

Abstract

To complete the study of Fredholm type operators of [10] and [11], we define in this paper the classes of left and right semi-B-Fredholm operators (Definition 3.1). Then, we prove that an operator $T\in L(X),X$ being a Banach space, is a left( resp. right) semi-B-Fredholm operator if and only if $T$ is the direct sum of left(resp. right) semi-Fredholm operator and a nilpotent one. This result extend the earlier characterization of B-Fredholm operators as the direct sum of a Fredholm operator and a nilpotent one obtained in [4,Theorem 2.7].

There is no difference with version 2, only an author whose name was forgotten in version 2 is added. arXiv admin note: text overlap with arXiv:2401.01390, arXiv:2401.01061