Ergodicity and mixing of W*-dynamical systems in terms of joinings

TL;DR

This paper investigates how ergodicity, weak mixing, and strong mixing in W*-dynamical systems can be characterized using joinings and subsystems, extending classical criteria to this operator algebra setting.

Contribution

It provides new characterizations of ergodic properties of W*-dynamical systems through joinings and subsystems, including Ornstein's criterion for strong mixing.

Findings

Characterizations of ergodicity, weak mixing, and strong mixing in terms of joinings

Extension of Ornstein's criterion to W*-dynamical systems

Analysis of subsystems related to mixing properties

Abstract

We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein's criterion for strong mixing are also discussed in this context.