Ergodic theory of amenable semigroup actions

TL;DR

This paper establishes a mean ergodic theorem for amenable semigroup algebras, advancing the understanding of ergodic properties in algebraic structures with amenability.

Contribution

It introduces and proves a mean ergodic theorem specifically for amenable semigroup algebras, a novel extension in ergodic theory.

Findings

Proved the mean ergodic theorem for amenable semigroup algebras

Extended ergodic theory to new algebraic structures

Provided foundational results for future research in this area

Abstract

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.