Operator spaces and residually finite-dimensional $C^{\ast }$-algebras

Abstract

For every operator space $X$ the $C^{\ast }$-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 $C^{\ast }$-algebra on any normed space so is. 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.

7 pages, AmS TeX 2.1