Noncommutative Ergodic Optimization and Unique Ergodicity

TL;DR

This paper extends ergodic optimization to non-commutative C*-dynamical systems and characterizes unique ergodicity using Choquet-theoretic assumptions, advancing understanding in non-commutative dynamics.

Contribution

It introduces a non-commutative ergodic optimization framework and offers a new characterization of unique ergodicity in C*-dynamical systems.

Findings

Extended ergodic optimization to C*-dynamical systems

Provided an alternative characterization of unique ergodicity

Applied Choquet-theoretic assumptions to non-commutative dynamics

Abstract

We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then employ this ergodic optimization machinery to provide an alternate characterization of unique erogdicity of C*-dynamical systems when the resident group action satisfies certain Choquet-theoretic assumptions.