Index of continuous semi-Fredholm families, regularities and semiregularities

TL;DR

This paper introduces an index for continuous families of semi-Fredholm operators and explores their regularities and semiregularities, advancing the understanding of operator families in functional analysis.

Contribution

It defines a new index for semi-Fredholm operator families and investigates their regularity properties, providing novel insights into their structure.

Findings

Defined an index for semi-Fredholm families

Analyzed regularities and semiregularities of operator families

Extended the theory of operator indices in functional analysis

Abstract

In this paper, we define and index for continuous families of semi-Fredholm bounded liner operators. Moreover, we study various regularities and semiregularities of continuous families of bounded linear operators.