On subclasses of Browder and Weyl operators

TL;DR

This paper introduces new subclasses of Browder and Weyl operators, explores their relationships with existing classes, and answers an open question in the operator theory literature.

Contribution

It defines the classes $(ab_{e})$ and $(aw_{e})$, establishes their connections with known classes, and provides an affirmative answer to a previously posed question.

Findings

Defined new subclasses $(ab_{e})$ and $(aw_{e})$ of Browder and Weyl operators.

Established relationships between these new classes and existing operator classes.

Provided an affirmative answer to an open question in the field.

Abstract

The main purpose of this paper, is to introduce and study the classes $(ab_{e})$ and $(aw_{e})$ which are strongly related to what has been recently studied in \cite{aznay-zariouh}. Furthermore, we give the connection between these classes and those that have been studied in \cite{berkani-zariouh0}. We also give an affirmative answer to a question asked in \cite{aznay-zariouh}.