Operator spaces and residually finite-dimensional \(C^*\)-algebras (Q1332192)

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. The proof is based on a criterion due to Exel and Loring.