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

TL;DR

This paper characterizes subalgebras and injective subspaces of continuous matrix-valued functions, with applications to sub-TROs and a specialized representation theorem, advancing the understanding of operator space structures.

Contribution

It provides an operator space characterization of subalgebras of $C(\,Omega,M_n)$ and introduces an $n$-minimal version of a key representation theorem.

Findings

Operator space characterization of subalgebras

Description of injective subspaces of $C(\,Omega,M_n)$

Application to sub-TROs and a new representation theorem

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.