A note on unital full amalgamated free products of RFD C∗-algebras

Abstract

In the paper, we consider the question whether a unital full amalgamated free product of RFD (residually finite dimensional) C^∗-algebras is RFD again. One example shows that the answer to the general case is no. We give a necessary and sufficient condition such that a unital full amalgamated free product of RFD C^∗-algebras with amalgamation over a finite dimensional C^∗-algebra is RFD. Applying this result, we conclude that a unital full free product of two same RFD C^∗-algebras with amalgamation over a finite-dimensional C^∗-algebra is always RFD.