M-ideals in real operator algebras
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912234766073856 |
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| author | Blecher, David P. Neal, Matthew Peralta, Antonio M. Su, Shanshan |
| author_facet | Blecher, David P. Neal, Matthew Peralta, Antonio M. Su, Shanshan |
| contents | In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples, including real C*-algebras, real JB*-algebras and real TROs, correspond to norm-closed triple ideals. In the present paper we extend this result to (possibly non-selfadjoint) real operator algebras and Jordan operator algebras, where the argument is necessarily different. We also give simple characterizations of one-sided M-ideals in real operator algebras, and give some applications to that theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | M-ideals in real operator algebras Blecher, David P. Neal, Matthew Peralta, Antonio M. Su, Shanshan Operator Algebras Functional Analysis Primary 46L07, 47L05, 47L25, 47L30, 17C65, Secondary: 46B04, 46L08, 47L75, 17C10 In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples, including real C*-algebras, real JB*-algebras and real TROs, correspond to norm-closed triple ideals. In the present paper we extend this result to (possibly non-selfadjoint) real operator algebras and Jordan operator algebras, where the argument is necessarily different. We also give simple characterizations of one-sided M-ideals in real operator algebras, and give some applications to that theory. |
| title | M-ideals in real operator algebras |
| topic | Operator Algebras Functional Analysis Primary 46L07, 47L05, 47L25, 47L30, 17C65, Secondary: 46B04, 46L08, 47L75, 17C10 |
| url | https://arxiv.org/abs/2405.05383 |