A study of weak$^*$-weak points of continuity in the unit ball of dual spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916787658948608 |
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| author | Daptari, S. Montesinos, V. Rao, T. S. S. R. K. |
| author_facet | Daptari, S. Montesinos, V. Rao, T. S. S. R. K. |
| contents | We study classes of Banach spaces where the points of weak$^*$-weak continuity for the identity mapping on the dual unit ball form a weak$^*$-dense and weak$^*$-$G_δ$ set. We also discuss how this property behaves in higher duals of Banach spaces. We prove in particular that if $\mathcal{A}$ is a von Neumann algebra and its predual has the Radon--Nikodým property, then there is no point of weak$^*$-weak continuity on the unit ball of $\mathcal{A}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A study of weak$^*$-weak points of continuity in the unit ball of dual spaces Daptari, S. Montesinos, V. Rao, T. S. S. R. K. Functional Analysis Primary 46A22, 46B10, 46B25, 47L40, Secondary 46B20, 46B22 We study classes of Banach spaces where the points of weak$^*$-weak continuity for the identity mapping on the dual unit ball form a weak$^*$-dense and weak$^*$-$G_δ$ set. We also discuss how this property behaves in higher duals of Banach spaces. We prove in particular that if $\mathcal{A}$ is a von Neumann algebra and its predual has the Radon--Nikodým property, then there is no point of weak$^*$-weak continuity on the unit ball of $\mathcal{A}$. |
| title | A study of weak$^*$-weak points of continuity in the unit ball of dual spaces |
| topic | Functional Analysis Primary 46A22, 46B10, 46B25, 47L40, Secondary 46B20, 46B22 |
| url | https://arxiv.org/abs/2506.08458 |