Projections in free product C*-algebras, II

1999/11/02 by Ken Dykema, Mikael Rordam · 2 citations
Mathematics · #math.OA #msc:46L05 #msc:46L35

paper · pdf

published as Math. Z. 234 (2000) pp. 103-113

arxiv created 1999/11/02 · arxiv updated 2009/11/30

Abstract

Let (A,phi) be the reduced free product of infinitely many pairs (A_i,phi_i) of C*-algebras with faithful states. Assume that the A_i 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.

Cited by

• Selfless reduced free products and graph products of C^∗-algebras
• Kaplansky's problem and unitary orbits in matrix amplifications

Related

• Projections in free product C*-algebras
• Purely infinite, simple C*-algebras arising from free product constructions, II
• Purely infinite, simple C*-algebras arising from free product constructions, III
• Reduced Free Products of Finite Dimensional C^*-Algebras
• Faithfulness of free product states