Tensor Products and Approximation Problems of $C^{\ast }$-Algebras

Abstract

For $C^{\ast }$-algebras $C$ and $D$ and their $C^{\ast }$-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 $C^{\ast }$-tensor product $C{\otimes }_{\alpha }D$ determines completely the subalgebra $A{\otimes }_{\alpha }B$. Relations to Effros' recent work are also discussed.