Index of continuous semi-Fredholm families, regularities and semiregularities

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.

This paper is a continuation of our papers: arxiv:1912.07267v1 and arxiv:2010.07040v1. The aim of these series of papers is to define an index for continuous Fredholm or semi-Fredholm families. Several applications are given through these papers, in particular a new generalization of Weyl theorem is obtained in the paper arxiv:1912.07267v1 for normal families acting on a Hilbert space. arXiv admin note: text overlap with arXiv:2010.07040