Projections in Free Product C {algebras
نویسنده
چکیده
Consider the reduced free product of C {algebras, (A; ') = (A 1 ; ' 1) (A 2 ; ' 2), with respect to states ' 1 and ' 2 that are faithful. If ' 1 and ' 2 are traces, if the so{called Avitzour conditions are satissed, (i.e. A 1 and A 2 are not \too small" in a speciic sense) and if A 1 and A 2 are nuclear, then it is shown that the positive cone, K 0 (A) + , of the K 0 {group of A consists of those elements g 2 K 0 (A) for which g = 0 or K 0 (')(g) > 0. Thus, the ordered group K 0 (A) is weakly unperforated. If, on the other hand, ' 1 or ' 2 is not a trace and if a certain condition weaker than the Avitzour conditions holds, then A is properly innnite.
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