The Space of Tracial States on a C$^*$-Algebra

TL;DR

This paper provides an elementary proof that the set of tracial states on a unital C*-algebra forms a Choquet simplex, utilizing the concept of center-valued trace on finite von Neumann algebras.

Contribution

It offers a simplified and elementary proof of a fundamental property of tracial state spaces in operator algebras.

Findings

Tracial state space is a Choquet simplex.

Elementary proof using center-valued trace.

Clarifies structure of tracial states on C*-algebras.

Abstract

We give a simple and elementary proof that the tracial state space of a unital C$^*$-algebra is a Choquet simplex, using the center-valued trace on a finite von Neumann algebra.