Morita equivalence and stable isomorphism via unitary operators
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908691328925696 |
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| author | Koutsonikos-Kouloumpis, Nikolaos |
| author_facet | Koutsonikos-Kouloumpis, Nikolaos |
| contents | We define $Δ$-equivalence for dual operator systems and prove that it is an equivalence relation. We show that weak TRO-equivalence of dual operator spaces induces a stable isomorphism between them which is given by multiplication with unitary operators, and in the special case of dual operator systems it is a unitary equivalence. We prove an analogous result for strong TRO-equivalence of operator spaces and for operator systems. Lastly, we show that $Δ$-equivalent dual operator spaces, considered as bimodules over their left and right adjointable multiplier algebras, have TRO-equivalent normal CES representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morita equivalence and stable isomorphism via unitary operators Koutsonikos-Kouloumpis, Nikolaos Operator Algebras We define $Δ$-equivalence for dual operator systems and prove that it is an equivalence relation. We show that weak TRO-equivalence of dual operator spaces induces a stable isomorphism between them which is given by multiplication with unitary operators, and in the special case of dual operator systems it is a unitary equivalence. We prove an analogous result for strong TRO-equivalence of operator spaces and for operator systems. Lastly, we show that $Δ$-equivalent dual operator spaces, considered as bimodules over their left and right adjointable multiplier algebras, have TRO-equivalent normal CES representations. |
| title | Morita equivalence and stable isomorphism via unitary operators |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2512.03956 |