Disjointness and unique ergodicity of C*-dynamical systems

Abstract

We study an ergodic theorem for disjoint C*-dynamical systems, where disjointness here is a noncommutative version of the concept introduced by Furstenberg for classical dynamical systems. This is applied to W*-dynamical systems. We also consider specific examples of disjoint C*-dynamical and W*-dynamical systems, including for actions of other groups than $\mathbb{Z}$. Unique ergodicity and unique ergodicity relative to the fixed point algebra are closely related to disjointness, and are used to give examples of disjoint C*-dynamical systems.

v1:18 pages. v2: Expanded version with greater emphasis on disjointness, 28 pages

References in corpus (3)

• Unique ergodicity of free shifts and some other automorphisms of C*-algebras
• Joinings of W*-dynamical systems
• Relatively independent joinings and subsystems of W*-dynamical systems