Subalgebras of $C(\Omega,M_n)$ and their modules

Abstract

We give an operator space characterization of subalgebras of $C(\Omega,M_n)$. We also describe injective subspaces of $C(\Omega,M_n)$ and then give applications to sub-TROs of $C(\Omega,M_n)$. Finally, we prove an `$n$-minimal version' of the Christensen-Effros-Sinclair representation theorem.