On generalizations of semi-Fredholm operators over C*-algebras

TL;DR

This paper explores various generalizations of semi-Fredholm operators over unital C*-algebras, extending existing theories to non-adjointable cases and broadening the mathematical framework of operator analysis.

Contribution

It introduces new generalizations of semi-Fredholm operators on C*-algebras, including non-adjointable cases, and extends previous results in the field.

Findings

Constructed various generalizations of semi-Fredholm operators.

Extended results to non-adjointable semi-A-Fredholm operators.

Provided analogues and generalizations of classical theorems in this setting.

Abstract

Starting from the definition of A-Fredholm and semi-A-Fredholm operator on the standard module over a unital C*- algebra A, introduced in [8] and [4], we construct various generalizations of these operators and obtain several results as an analogue or a generalization of the results in [1], [2], [3],[7]. Moreover, we study also non-adjointable semi-A-Fredholm operators as a natural continuation of the work in [6] on non-adjointable A-Fredholm operators and obtain an analogue or a generalization in this setting of the results in [4], [5].