Morita equivalence for operator systems
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866908854268198912 |
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| author | Eleftherakis, George K. Kakariadis, Evgenios T. A. Todorov, Ivan G. |
| author_facet | Eleftherakis, George K. Kakariadis, Evgenios T. A. Todorov, Ivan G. |
| contents | We define $Δ$-equivalence for operator systems and show that it is identical to stable isomorphism. We define $Δ$-contexts and bihomomorphism contexts and show that two operator systems are $Δ$-equivalent if and only if they can be placed in a $Δ$-context, equivalently, in a bihomomorphism context. We show that nuclearity for a variety of tensor products is an invariant for $Δ$-equivalence and that function systems are $Δ$-equivalent precisely when they are order isomorphic. We prove that $Δ$-equivalent operator systems have equivalent categories of representations. As an application, we characterise $Δ$-equivalence of graph operator systems in combinatorial terms. We examine a notion of Morita embedding for operator systems, showing that mutually $Δ$-embeddable operator systems have orthogonally complemented $Δ$-equivalent corners when represented in the double dual of their C*-envelopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_12031 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Morita equivalence for operator systems Eleftherakis, George K. Kakariadis, Evgenios T. A. Todorov, Ivan G. Operator Algebras 47L25, 46L07 We define $Δ$-equivalence for operator systems and show that it is identical to stable isomorphism. We define $Δ$-contexts and bihomomorphism contexts and show that two operator systems are $Δ$-equivalent if and only if they can be placed in a $Δ$-context, equivalently, in a bihomomorphism context. We show that nuclearity for a variety of tensor products is an invariant for $Δ$-equivalence and that function systems are $Δ$-equivalent precisely when they are order isomorphic. We prove that $Δ$-equivalent operator systems have equivalent categories of representations. As an application, we characterise $Δ$-equivalence of graph operator systems in combinatorial terms. We examine a notion of Morita embedding for operator systems, showing that mutually $Δ$-embeddable operator systems have orthogonally complemented $Δ$-equivalent corners when represented in the double dual of their C*-envelopes. |
| title | Morita equivalence for operator systems |
| topic | Operator Algebras 47L25, 46L07 |
| url | https://arxiv.org/abs/2109.12031 |