Spectrum of Weighted Composition Operators Part VII Essential spectra of weighted composition operators on $C(K)$. The case of non-invertible homeomorphisms

TL;DR

This paper characterizes the spectrum and essential spectra of weighted composition operators on continuous functions over a compact space, specifically when the underlying map is a non-invertible homeomorphism.

Contribution

It provides a complete spectral description of weighted composition operators with non-invertible homeomorphisms on $C(K)$.

Findings

Complete description of spectrum and essential spectra

Applicable to non-invertible homeomorphisms

Advances understanding of weighted composition operators

Abstract

We provide a complete description of the spectrum and the essential spectra of weighted composition operators $T=wT_\varphi$ on $C(K)$ in the case when the map $\varphi$ is a non-invertible homeomorphism of $K$ into itself.