Commuting contractive idempotents in measure algebras

TL;DR

This paper characterizes when contractive idempotents in measure algebras of locally compact groups commute and explores related dynamical properties and measure groups.

Contribution

It provides a complete characterization of commuting contractive idempotents and investigates properties of measure groups with such idempotents.

Findings

Identifies conditions for commutativity of contractive idempotents

Analyzes dynamical aspects related to these idempotents

Studies properties of groups of measures with a contractive idempotent as identity

Abstract

We determine when contractive idempotents in the measure algebra of a locally compact group commute. We consider a dynamical version of the same result. We also look at some properties of groups of measures whose identity is a contactive idempotent.