Relatively independent joinings and subsystems of W*-dynamical systems

TL;DR

This paper constructs relatively independent joinings of W*-dynamical systems and explores their relation to subsystems, providing new characterizations of weak mixing, ergodicity, and compactness in these systems.

Contribution

It introduces a method to construct joinings and links them to subsystem properties, offering novel characterizations of dynamical behaviors.

Findings

Characterization of weak mixing via joinings

Description of fixed point and compact subsystems

New insights into relative ergodicity

Abstract

Relatively independent joinings of W*-dynamical systems are constructed. This is intimately related to subsystems of W*-dynamical systems, and therefore we also study general properties of subsystems, in particular fixed point subsystems and compact subsystems. This allows us to obtain characterizations of weak mixing and relative ergodicity, as well as of certain compact subsystems, in terms of joinings.