On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911402659151872 |
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| author | Gaebler, Harrison Motakis, Pavlos Sari, Bunyamin |
| author_facet | Gaebler, Harrison Motakis, Pavlos Sari, Bunyamin |
| contents | We construct a reflexive Banach space $X_\mathcal{D}$ with an unconditional basis such that all spreading models admitted by normalized block sequences in $X_\mathcal{D}$ are uniformly equivalent to the unit vector basis of $\ell_1$, yet every infinite-dimensional closed subspace of $X_\mathcal{D}$ fails the Lebesgue property. This is a new result in a program initiated by Odell in 2002 concerning the strong separation of asymptotic properties in Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces Gaebler, Harrison Motakis, Pavlos Sari, Bunyamin Functional Analysis 46B06, 46B20, 46B25, 46G12 We construct a reflexive Banach space $X_\mathcal{D}$ with an unconditional basis such that all spreading models admitted by normalized block sequences in $X_\mathcal{D}$ are uniformly equivalent to the unit vector basis of $\ell_1$, yet every infinite-dimensional closed subspace of $X_\mathcal{D}$ fails the Lebesgue property. This is a new result in a program initiated by Odell in 2002 concerning the strong separation of asymptotic properties in Banach spaces. |
| title | On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces |
| topic | Functional Analysis 46B06, 46B20, 46B25, 46G12 |
| url | https://arxiv.org/abs/2402.14687 |