On locally finite dimensional traces

Abstract

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 $C_r^{\ast }(\Gamma )$ of a discrete amenable ICC group $\Gamma$ are uniformly LFD, and conclude that $C_r^{\ast }(\Gamma )$ is strong-NF in the sense of Blackadar-Kirchberg in this case. This partially answers another open question raised by Brown.

arXiv comment10 pages, comments are welcome!