Disjointness and unique ergodicity of C*-dynamical systems

Details Disjointness and unique ergodicity of C*-dynamical systems Disjointness and unique ergodicity of C*-dynamical systems

2011-02-21

arxiv.org/abs/1102.4243v2

Mathematics

Operator Algebras

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

Scientific paper

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.

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