Joinings of W*-dynamical systems

TL;DR

This paper explores the concept of joinings in W*-dynamical systems, establishing conditions for ergodicity and examining related conditional expectation operators, thus extending ideas from measure theoretic ergodic theory to operator algebras.

Contribution

It introduces a framework for understanding joinings in W*-dynamical systems and characterizes ergodicity through these joinings, bridging measure theory and operator algebras.

Findings

Necessary and sufficient conditions for ergodicity via joinings

Analysis of conditional expectation operators associated with joinings

Extension of measure theoretic ergodic theory concepts to W*-dynamical systems

Abstract

We study the notion of joinings of W*-dynamical systems, building on ideas from measure theoretic ergodic theory. In particular we prove sufficient and necessary conditions for ergodicity in terms of joinings, and also briefly look at conditional expectation operators associated with joinings.