What does a rate in a mean ergodic theorem imply?

TL;DR

This paper develops a comprehensive framework for inverse mean ergodic theorems with rates for operator semigroups, advancing the theoretical understanding of ergodic behavior in mathematical analysis.

Contribution

It introduces a general framework for inverse mean ergodic theorems with rates, completing previous theoretical constructions.

Findings

Established a unified approach to inverse mean ergodic theorems with rates.

Extended the theory of operator semigroups in ergodic analysis.

Provided new tools for analyzing convergence rates in ergodic theorems.

Abstract

We develop a general framework for the inverse mean ergodic theorems with rates for operator semigroups thus completing a construction of the theory initiated in [16] and [17].