Projections in free product C*-algebras
Abstract
Consider the reduced free product of C*-algebras, (A,φ)=(A1,φ1)*(A2,φ2), with respect to states φ1 and φ2 that are faithful. If φ1 and φ2 are traces, if the so-called Avitzour conditions are satisfied, (i.e. A1 and A2 are not ``too small'' in a specific sense) and if A1 and A2 are nuclear, then it is shown that the positive cone of the K0-group of A consists of those elements g in K0(A) for which g=0 or K0(φ)(g)>0. Thus, the ordered group K0(A) is weakly unperforated. If, on the other hand, φ1 or φ2 is not a trace and if a certain condition weaker than the Avitzour conditions hold, then A is properly infinite.
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