Classification of homomorphisms and dynamical systems
Classification of homomorphisms and dynamical systems
Let $A$ be a unital simple $C^*$-algebra, with tracial rank zero and let $X$ be a compact metric space. Suppose that $h_1, h_2: C(X)\to A$ are two unital monomorphisms. We show that $h_1$ and $h_2$ are approximately unitarily equivalent if and only if \[ [h_1]=[h_2] \textrm {in} KL(C(X),A) \textrm {and} …