Noncommutative Ergodic Optimization
Operator Algebras
2023-03-30 v2 Dynamical Systems
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.
Cite
@article{arxiv.2302.06109,
title = {Noncommutative Ergodic Optimization},
author = {Aidan Young},
journal= {arXiv preprint arXiv:2302.06109},
year = {2023}
}
Comments
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