Uniform families of ergodic operator nets

TL;DR

This paper investigates mean ergodicity in amenable operator semigroups, linking convergence of ergodic nets to topological Wiener-Wintner theorems, and introduces uniform families of ergodic nets.

Contribution

It establishes the connection between mean ergodicity and convergence of ergodic nets, and demonstrates convergence of uniform families in topological Wiener-Wintner theorems.

Findings

Proves the connection between mean ergodicity and ergodic net convergence.

Shows convergence of uniform families of ergodic nets in specific theorems.

Provides new insights into ergodic theory for operator semigroups.

Abstract

We study mean ergodicity in amenable operator semigroups and establish the connection to the convergence of strong and weak ergodic nets. We then use these results in order to show the convergence of uniform families of ergodic nets that appear in topological Wiener-Wintner theorems.