Relatively independent joinings and subsystems of W*-dynamical systems

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.

22 pages

References in corpus (4)

• Joinings of W*-dynamical systems
• The Szemeredi property in ergodic W*-dynamical systems
• Ergodicity and mixing of W*-dynamical systems in terms of joinings
• Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems

Cited by in corpus (12)

• Balance between quantum Markov semigroups
• $C^{\ast }$-fermi systems and detailed balance
• Wasserstein distance between noncommutative dynamical systems
• Relative ergodic properties of C*-dynamical systems
• Weak mixing for locally compact quantum groups
• Extending quantum detailed balance through optimal transport
• Ergodic theory for quantum semigroups
• Relative weak mixing of W*-dynamical systems via joinings
• Disjointness and unique ergodicity of C*-dynamical systems
• The Modular Symmetry of Markov Maps
• Relative discrete spectrum of W*-dynamical systems
• On Noncommutative Joinings