On preservers of strong Birkhoff-James orthogonality between $C^*$-algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908617126445056 |
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| author | Kuzma, Bojan Stefanović, Srdjan Tanaka, Ryotaro |
| author_facet | Kuzma, Bojan Stefanović, Srdjan Tanaka, Ryotaro |
| contents | It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of (possibly nonlinear) strong Birkhoff-James isomorphisms between compact $C^*$-algebras are determined. A nonlinear characterization of compact $C^*$-algebras in terms of strong Birkhoff-James orthogonality is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On preservers of strong Birkhoff-James orthogonality between $C^*$-algebras Kuzma, Bojan Stefanović, Srdjan Tanaka, Ryotaro Operator Algebras Primary 46L05, Secondary 46L35, 46B20, 46B80, 47B49 It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of (possibly nonlinear) strong Birkhoff-James isomorphisms between compact $C^*$-algebras are determined. A nonlinear characterization of compact $C^*$-algebras in terms of strong Birkhoff-James orthogonality is also given. |
| title | On preservers of strong Birkhoff-James orthogonality between $C^*$-algebras |
| topic | Operator Algebras Primary 46L05, Secondary 46L35, 46B20, 46B80, 47B49 |
| url | https://arxiv.org/abs/2510.24308 |