A simple proof of a theorem of kirchberg and related results on C<sup>*</sup>-norms

Let F be a free group and let C*(F) be the (full) C*-algebra of F. We give a simple proof of Kirdtberg's theorem that there is only one C*-norm on the algebraic tensor product C*(F)B(H), or equivalently that C*(F) min B(H) = C*(F) max B(H). More generally, let A be the (unital) free product of a family (Ai)iiGI of (unital) C*-algebras. We show that if Ai min B(H) = Ai max B(H) holds for all i in I, then A min B(H) = Amax B(H). Thete, 1996.

A simple proof of a theorem of kirchberg and related results on C^*-norms Academic Article