On locally finite‐dimensional traces

Abstract

AbstractWe partially resolve two open questions on approximation properties of traces on simple ‐algebras. We answer a question raised by Nate Brown by showing that locally finite‐dimensional (LFD) traces form a convex set for simple ‐algebras. We prove that all the traces on the reduced ‐algebra of a discrete amenable ICC group are LFD, and conclude that is strong‐NF in the sense of Blackadar–Kirchberg in this case. This partially answers another open question raised by Brown.