Joinings of 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.

11 pages

Cited by in corpus (14)

• Relatively independent joinings and subsystems of W*-dynamical systems
• Balance between quantum Markov semigroups
• $C^{\ast }$-fermi systems and detailed balance
• Detailed balance and entanglement
• Wasserstein distance between noncommutative dynamical systems
• Extending quantum detailed balance through optimal transport
• Fermionic quantum detailed balance and entanglement
• Relative weak mixing of W*-dynamical systems via joinings
• On tensor products of weak mixing vector sequences and their applications to uniquely $E$-weak mixing $C^{\ast }$- dynamical systems
• Free joinings of C*-dynamical systems
• Ergodicity and mixing of W*-dynamical systems in terms of joinings
• The Modular Symmetry of Markov Maps
• Disjointness and unique ergodicity of C*-dynamical systems
• On Noncommutative Joinings