Tensor Products and Approximation Problems of <i>C</i>*-Algebras

Abstract

For C*-algebras C and D and their C*-subalgebras A and B, it is shown with other related results that if all irreducible representations of A are finite dimensional with bounded degree then the family of product functionals in the minimal C*-tensor product C_⊗_D determines completely the subalgebra A®B. Relations to Effros' recent work are also discussed.