On the index of pseudo B-Fredholm operator

TL;DR

This paper introduces a generalized index for pseudo B-Fredholm operators, extending classical Fredholm theory concepts like nullity, deficiency, ascent, and descent to this broader class.

Contribution

It defines the index for pseudo B-Fredholm operators and extends key Fredholm properties to this new setting, broadening the scope of operator theory.

Findings

Defined the index for pseudo B-Fredholm operators

Extended nullity, deficiency, ascent, and descent concepts

Generalized classical Fredholm results to pseudo B-Fredholm operators

Abstract

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the deficiency, the ascent and the descent will be extended and defined for a pseudo-Fredholm operator.