Inverse-closed algebras of integral operators on locally compact groups

TL;DR

This paper constructs inverse-closed algebras of integral operators with operator-valued kernels on locally compact groups, utilizing covariance algebras from $C^*$-dynamical systems to analyze their properties.

Contribution

It introduces a systematic method to build inverse-closed algebras of integral operators using covariance algebras related to $C^*$-dynamical systems on locally compact groups.

Findings

Established inverse-closed algebras for integral operators with operator-valued kernels

Utilized covariance algebras associated with $C^*$-dynamical systems

Provided a framework for analyzing bounded integral operators on groups

Abstract

We construct some inverse-closed algebras of bounded integral operators with operator-valued kernels, acting in spaces of vector-valued functions on locally compact groups. To this end we make systematic use of covariance algebras associated to $C^*$-dynamical systems defined by the abelian $C^*$-algebras of right uniformly continuous functions with respect to the left regular representation.