Primitivity of unital full free products of residually finite dimensional C*-algebras

A C*-algebra is called primitive if it admits a faithful and irreducible *-representation. We show that if A(1) and A(2) are separable, unital, residually finite dimensional C*-algebras satisfying (dim(A(1)) - 1)(dim(A(2)) - 1) >= 2, then the unital C*-algebra full free product, A = A(1) * A(2) is primitive. It follows that A is antiliminal, it has an uncountable family of pairwise inequivalent irreducible faithful *-representations and the set of pure states is w*-dense in the state space. (C) 2014 Elsevier Inc. All rights reserved.