Inverse-closed algebras of integral operators on locally compact 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.

22 pages; accepted for publication in Annales Henri Poincare