The Dixmier Property and Tracial States for C^*-Algebras

Abstract

Let A is a C^*-algebra for which A≅A ⊗ Z, where Z is the Jiang–Su algebra: a unital, simple, stably finite, separable, nuclear, infinite-dimensional C^*-algebra . We show that every directed graph defines a Hilbert space and a family of weighted shifts that act on the space.We obtain necessary and sufficient conditions for a simple unital C^*-algebra with unique tracial state to have this uniform property.