An extension property for noncommutative convex sets and duality for operator systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909721172115456 |
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| author | Humeniuk, Adam Kennedy, Matthew Manor, Nicholas |
| author_facet | Humeniuk, Adam Kennedy, Matthew Manor, Nicholas |
| contents | We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an application of this result, we obtain a simple geometric characterization of (possibly nonunital) operator systems that are dualizable, meaning that their dual can be equipped with an operator system structure. We further establish some permanence properties of dualizability, and provide a large new class of dualizable operator systems. These results are new even when specialized to ordinary compact convex sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04791 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An extension property for noncommutative convex sets and duality for operator systems Humeniuk, Adam Kennedy, Matthew Manor, Nicholas Operator Algebras Functional Analysis 46A55, 46L07, 46L52, 47L25, 47L50 We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an application of this result, we obtain a simple geometric characterization of (possibly nonunital) operator systems that are dualizable, meaning that their dual can be equipped with an operator system structure. We further establish some permanence properties of dualizability, and provide a large new class of dualizable operator systems. These results are new even when specialized to ordinary compact convex sets. |
| title | An extension property for noncommutative convex sets and duality for operator systems |
| topic | Operator Algebras Functional Analysis 46A55, 46L07, 46L52, 47L25, 47L50 |
| url | https://arxiv.org/abs/2312.04791 |