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arXiv · 2606.25531

On Subhomogeneous Operator Systems

Markus Dannemüller·Tim Netzer
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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.

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Markus Dannemüller, Tim Netzer. 2026-06-24. On Subhomogeneous Operator Systems. https://arxiv.org/abs/2606.25531

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