Relative ergodic properties of C*-dynamical systems

TL;DR

This paper investigates ergodic properties of C*-dynamical systems, focusing on relative ergodicity and weighted means, providing characterizations, ergodic theorems, and illustrative examples.

Contribution

It introduces a framework for relative ergodic properties in C*-dynamical systems, extending classical concepts with new characterizations and examples.

Findings

Characterization of relative ergodic properties

Ergodic theorems derived from these properties

Examples demonstrating the properties

Abstract

We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main results are characterizations of such relative ergodic properties, ergodic theorems resulting from these properties, and examples exhibiting these properties.