2021/09/28 by Aidan Young, Young, Aidan
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Analysis #Operator Algebras (math.OA) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2109.13965
openalex publication_date 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous article, we extended the notion of ergodic optimization to the setting of C*-dynamical systems of countable discrete groups. Among the key results of that paper was that given an action G \stackrelΞ\curvearrowright \mathfrakM of a countable discrete amenable group G on a W*-probability space (\mathfrakM, ρ) by ρ-preserving *-automorphisms of \mathfrakM, a positive element x ∈ \mathfrakM, and a right Følner sequence F = (Fk)k ∈ ℕ for G, the sequence ( ‖ (1)/(|Fk|) ∑g ∈ Fk Ξg x ‖ ) k ∈ ℕ converges to a value Γ(x) which can be described in the language of ergodic optimization. We provide here an alternate, more direct proof of that theorem using the tools of nonstandard analysis.