On Subhomogeneous Operator Systems

Abstract

We study subhomogeneity for finite-dimensional operator systems, and collect and extend characterizations in terms of the $C^*$-envelope, $d$-maximality, complete positivity, dual $d$-minimality, and non-commutative boundary conditions. We then show that the dual of a subhomogeneous operator system, while not necessarily subhomogeneous itself, is always a quotient of a subhomogeneous system. We complement these characterizations with examples and counterexamples, including minimal and maximal systems over certain polyhedral cones.