Spectra of weighted composition operators induced by automorphisms

TL;DR

This paper investigates the spectra of non-invertible weighted composition operators induced by automorphisms on various Hilbert spaces, providing new insights into their spectral properties.

Contribution

It offers novel results on the spectra of these operators on Hardy and weighted Bergman spaces, expanding understanding of their spectral behavior.

Findings

Spectra characterized for operators on Hardy space

Spectral properties analyzed on weighted Bergman spaces

Results applicable to non-invertible automorphism-induced operators

Abstract

In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\mathbb{D})$ and weighted Bergman spaces $A_\alpha^2(\mathbb{D})$.