FREE PRODUCTS WITH AMALGAMATION OVER CENTRAL C*-SUBALGEBRAS

Let A and B be C*-algebras whose quotients are all RFD (residually finite dimensional), and let C be a central C*-subalgebra in both A and B. We prove that the full amalgamated free product A(*C) B is then RFD. This generalizes Korchagin's result that amalgamated free products of commutative C*-algebras are RFD. When applied to the case of trivial amalgam, our methods recover the result of Exel and Loring for separable C*-algebras. As corollaries to our theorem, we give sufficient conditions for amalgamated free products of maximally almost periodic (MAP) groups to have RFD C*-algebras and hence to be MAP.