Spectrum of weighted composition operators. Part VIII. Lower semi-Fredholm and Fredholm spectra of weighted compositions on $C(K)$, case of non-invertible surjections

TL;DR

This paper characterizes when weighted composition operators on $C(K)$ are lower semi-Fredholm or Fredholm, focusing on non-invertible surjections and involving almost homeomorphisms of compact spaces.

Contribution

It provides new criteria for Fredholm properties of weighted composition operators on $C(K)$ with non-invertible surjective maps.

Findings

Criteria for lower semi-Fredholm and Fredholm operators on $C(K)$

Involvement of almost homeomorphisms in the characterization

Focus on non-invertible surjective maps

Abstract

We characterize lower semi-Fredholm and Fredholm of weighted composition operators on $C(K)$ in the case when the corresponding map is an open surjection of the compact space $K$ onto itself. The obtained criterions involve the notion of almost homeomorphisms of compact spaces.