The Cuntz semigroup of continuous functions into certain simple C*-algebras

Abstract

This paper contains computations of the Cuntz semigroup of separable C*-algebras of the form C_0(X,A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murray-von Neumann semigroups of C(K,A) for compact subsets K of X. In particular, the computation shows that the Elliott invariant is functorially equivalent to the invariant given by the Cuntz semigroup of C(T,A). These results are a contribution towards the goal of using the Cuntz semigroup in the classification of well-behaved non-simple C*-algebras.