On subspaces whose weak* derived sets are proper and norm dense
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917738787635200 |
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| author | Silber, Zdeněk |
| author_facet | Silber, Zdeněk |
| contents | We study long chains of iterated weak* derived sets, that is sets of all weak* limits of bounded nets, of subspaces with the additional property that the penultimate weak* derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak* derived set of order α is proper and norm dense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_00288 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On subspaces whose weak* derived sets are proper and norm dense Silber, Zdeněk Functional Analysis 46B10, 46B20 We study long chains of iterated weak* derived sets, that is sets of all weak* limits of bounded nets, of subspaces with the additional property that the penultimate weak* derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak* derived set of order α is proper and norm dense. |
| title | On subspaces whose weak* derived sets are proper and norm dense |
| topic | Functional Analysis 46B10, 46B20 |
| url | https://arxiv.org/abs/2203.00288 |