Projections in free product C*algebras
Abstract
Consider the reduced free product of C*algebras, (A,\phi)=(A_1,\phi_1)*(A_2,\phi_2), with respect to states \phi_1 and \phi_2 that are faithful. If \phi_1 and \phi_2 are traces, if the socalled Avitzour conditions are satisfied, (i.e. A_1 and A_2 are not ``too small'' in a specific sense) and if A_1 and A_2 are nuclear, then it is shown that the positive cone of the K_0group of A consists of those elements g in K_0(A) for which g=0 or K_0(\phi)(g)>0. Thus, the ordered group K_0(A) is weakly unperforated. If, on the other hand, \phi_1 or \phi_2 is not a trace and if a certain condition weaker than the Avitzour conditions hold, then A is properly infinite.
 Publication:

arXiv eprints
 Pub Date:
 February 1997
 DOI:
 10.48550/arXiv.functan/9702016
 arXiv:
 arXiv:functan/9702016
 Bibcode:
 1997funct.an..2016D
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras;
 46L80 (19K14;
 46L05;
 46L35)