On Left and Right Semi-B-Fredholm Operators

Alaa Hamdan; Mohammed Berkani

On Left and Right Semi-B-Fredholm Operators

Functional Analysis 2024-03-06 v3

Authors: Alaa Hamdan , Mohammed Berkani

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].

Keywords

fredholm operators operator theory

Cite

@article{arxiv.2402.09261,
  title  = {On Left and Right Semi-B-Fredholm Operators},
  author = {Alaa Hamdan and Mohammed Berkani},
  journal= {arXiv preprint arXiv:2402.09261},
  year   = {2024}
}

Comments

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

On Left and Right Semi-B-Fredholm Operators

Abstract

Keywords

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