A Kaplansky Theorem for JB*-triples
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911769010634752 |
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| author | Fernández-Polo, Francisco J. Garcés, Jorge J. Peralta, Antonio M. |
| author_facet | Fernández-Polo, Francisco J. Garcés, Jorge J. Peralta, Antonio M. |
| contents | Let $T:E\rightarrow F$ be a non-necessarily continuous triple homomorphism from a (complex) JB$^*$-triple (respectively, a (real) J$^*$B-triple) to a normed Jordan triple. The following statements hold:
(1) $T$ has closed range whenever $T$ is continuous
(2) $T$ has closed range whenever $T$ is continuous
This result generalises classical theorems of I. Kaplansky and S.B. Cleveland in the setting of C$^*$-algebras and of A. Bensebah and J.Pérez, L. Rico and A. Rodr'\iguez Palacios in the setting of JB$^*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Kaplansky Theorem for JB*-triples Fernández-Polo, Francisco J. Garcés, Jorge J. Peralta, Antonio M. Operator Algebras Functional Analysis Let $T:E\rightarrow F$ be a non-necessarily continuous triple homomorphism from a (complex) JB$^*$-triple (respectively, a (real) J$^*$B-triple) to a normed Jordan triple. The following statements hold: (1) $T$ has closed range whenever $T$ is continuous (2) $T$ has closed range whenever $T$ is continuous This result generalises classical theorems of I. Kaplansky and S.B. Cleveland in the setting of C$^*$-algebras and of A. Bensebah and J.Pérez, L. Rico and A. Rodr'\iguez Palacios in the setting of JB$^*$-algebras. |
| title | A Kaplansky Theorem for JB*-triples |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2402.00538 |