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arXiv · 2005.11582

Strongly peaking representations and compressions of operator systems

Kenneth R. Davidson·Benjamin Passer
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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.

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Kenneth R. Davidson, Benjamin Passer. 2020-05-23. Strongly peaking representations and compressions of operator systems. https://doi.org/10.1093/imrn/rnaa228

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