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

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.