Title: Commutative ${C}^*$-subalgebras of simple stably finite ${C}^*$-algebras with real rank zero

Authors: Ping Wong Ng and Wilhelm Winter

Issue: Volume 57 (2008), Issue 7, 3209-3240

Abstract: Let $X$ be a second countable, path connected, compact metric space and let $A$ be a unital separable simple nuclear $\mathcal{Z}$-stable real rank zero $C^{*}$-algebra. We classify all the unital $*$-embeddings (up to approximate unitary equivalence) of $C(X)$ into $A$. Specifically, we provide an existence and a uniqueness theorem for unital $*$-embeddings from $C(X)$ into $A$.