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

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.

v1: 9 pages. v2: Extended by 2 sections (Sections 3 and 5), with small changes/corrections elsewhere and a more descriptive title; 22 pages. v3: Improved results in Sections 4 and 5; 24 pages

References in corpus (5)

• Locally Compact Quantum Groups. A von Neumann Algebra Approach
• Joinings of W*-dynamical systems
• Bergelson's Theorem for weakly mixing C*-dynamical systems
• The Szemeredi property in ergodic W*-dynamical systems
• The entangled ergodic theorem and an ergodic theorem for quantum "diagonal measures"

Cited by in corpus (1)

• Relatively independent joinings and subsystems of W*-dynamical systems