2022/04/19 by Massoud Amini, Amini, Massoud, Mehdi Moradi +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2204.08738
openalex publication_date 2022/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We partially resolve three open questions on approximation properties of traces on simple C*-algebras. We partially answer two questions raised by Nate Brown by showing that locally finite dimensional (LFD) traces form a convex set on simple C*-algebras and that they are automatically uniformly LFD on locally reflexive C*-algebras. We prove that all the traces on the reduced \C-algebra C^*r(Γ) of a discrete amenable ICC group Γ are uniformly LFD, and conclude that C^*r(Γ) is strong-NF in the sense of Blackadar-Kirchberg in this case. This partially answers another open question raised by Brown.