Strongly peaking representations and compressions of operator systems
Operator Algebras
2022-04-21 v2 Functional Analysis
Abstract
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates the C*-envelope and is such that the identity is the direct sum of strongly peaking representations. In particular, a fully compressed presentation of a separable operator system is unique up to unitary equivalence. Under various additional assumptions, minimality conditions are sufficient to determine a separable operator system uniquely.
Cite
@article{arxiv.2005.11582,
title = {Strongly peaking representations and compressions of operator systems},
author = {Kenneth R. Davidson and Benjamin Passer},
journal= {arXiv preprint arXiv:2005.11582},
year = {2022}
}
Comments
26 pages. Version 2 has minor updates. To appear in International Mathematics Research Notices