Projections in free product C*-algebras, II
Ken Dykema, Mikael Rordam
Abstract
Let (A,phi) be the reduced free product of infinitely many pairs (Ai,phii) of C*-algebras with faithful states. Assume that the Ai are not too small, in a specific sense. It is shown that if phi is a trace then K0(A) is determined entirely by K0(phi). If, furthermore, the image of K0(phi) is dense in the reals then A has real rank zero. On the other hand, if phi is not a trace then A is simple and purely infinite.
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