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Projections in free product C*-algebras

Kenneth J. Dykema, Mikael Rordam

funct-anarXiv:funct-an/9702016

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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