Strict comparison and $ \mathcal{Z} $-absorption of nuclear C∗-algebras

Abstract

For any unital separable simple infinite-dimensional nuclear C^∗-algebra with finitely many extremal traces, we prove that $ \mathcal{Z} $-absorption, strict comparison and property (SI) are equivalent. We also show that any unital separable simple nuclear C^∗-algebra with tracial rank zero is approximately divisible, and hence is $ \mathcal{Z} $-absorbing.