A missing theorem on dual spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929338914439168 |
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| author | Blecher, David P. |
| author_facet | Blecher, David P. |
| contents | We answer in the affirmative the surprisingly difficult questions: If a complex Banach space possesses a real predual X, then is X a complex Banach space?
If a complex Banach space possesses a real predual, then does it have a complex predual? We also answer the analogous questions for operator spaces, that is spaces of operators on a Hilbert space, up to complete isometry. Indeed we use operator space methods to solve the Banach space question above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A missing theorem on dual spaces Blecher, David P. Functional Analysis Classical Analysis and ODEs Operator Algebras We answer in the affirmative the surprisingly difficult questions: If a complex Banach space possesses a real predual X, then is X a complex Banach space? If a complex Banach space possesses a real predual, then does it have a complex predual? We also answer the analogous questions for operator spaces, that is spaces of operators on a Hilbert space, up to complete isometry. Indeed we use operator space methods to solve the Banach space question above. |
| title | A missing theorem on dual spaces |
| topic | Functional Analysis Classical Analysis and ODEs Operator Algebras |
| url | https://arxiv.org/abs/2405.01133 |