Operator Spaces and Residually Finite-Dimensional C*-Algebras

For every operator space X the C*-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In particular, the free C*-algebra on any normed space is residually finite-dimensional. This is an extension of an earlier result by Goodearl and Menal, and our short proof is based on a criterion due to Exel and Loring.