Noncommutative Ergodic Optimization

Abstract

We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of certain ergodic averages in a suitable seminorm. We also provide alternate proofs of several results in this article using the tools of nonstandard analysis.

This article is derived from a chapter of the author's doctoral dissertation. It combines and extends two articles previously uploaded to the arXiv:2109.10425 and arXiv:2109.13965. This version corrects a few minor typos found in the first version