Octahedrality and Gâteaux smoothness
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914903892164608 |
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| author | Cobollo, Ch. Hájek, P. |
| author_facet | Cobollo, Ch. Hájek, P. |
| contents | We prove that every Banach space admitting a Gateaux smooth norm and containing a complemented copy of $\ell_1$ has an equivalent renorming which is simultaneously Gâteaux smooth and octahedral. This is a partial solution to a problem from the early nineties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Octahedrality and Gâteaux smoothness Cobollo, Ch. Hájek, P. Functional Analysis 46B03, 46B20, 46B26 We prove that every Banach space admitting a Gateaux smooth norm and containing a complemented copy of $\ell_1$ has an equivalent renorming which is simultaneously Gâteaux smooth and octahedral. This is a partial solution to a problem from the early nineties. |
| title | Octahedrality and Gâteaux smoothness |
| topic | Functional Analysis 46B03, 46B20, 46B26 |
| url | https://arxiv.org/abs/2408.03737 |