Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914662765821952 |
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| author | Burgos, María Garcés, Jorge J. Peralta, Antonio M. |
| author_facet | Burgos, María Garcés, Jorge J. Peralta, Antonio M. |
| contents | We prove that every biorthogonality preserving linear surjection from a weakly compact JB$^*$triple containing no infinite dimensional rank-one summands onto another JB$^*$-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW$^*$triples containing no infinite dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW$^*$-triples containing no rank-one summands are isomorphic if, and only if, there exists a (non necessarily continuous) biorthogonality preserving linear surjection between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples Burgos, María Garcés, Jorge J. Peralta, Antonio M. Operator Algebras Functional Analysis We prove that every biorthogonality preserving linear surjection from a weakly compact JB$^*$triple containing no infinite dimensional rank-one summands onto another JB$^*$-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW$^*$triples containing no infinite dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW$^*$-triples containing no rank-one summands are isomorphic if, and only if, there exists a (non necessarily continuous) biorthogonality preserving linear surjection between them. |
| title | Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2402.00517 |