Weakly centered weighted composition operators in $L^2$-spaces

TL;DR

This paper characterizes weakly centered and spectrally weakly centered weighted composition operators in $L^2$-spaces, providing criteria for invariant subspaces and supporting results with examples.

Contribution

It introduces new characterizations and criteria for weakly centered operators in $L^2$-spaces, expanding understanding of their spectral properties.

Findings

Characterization of weakly centered weighted composition operators

Criteria for existence of invariant subspaces

Examples illustrating the theoretical results

Abstract

Weakly centered and spectrally weakly cenetered weighted composition operators in $L^2$-spaces are characterized. Criteria for existence of invariant subspaces are given. Additional results and examples are supplied.