The strong Nakano property in Banach lattices
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929226257530880 |
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| author | Azouzi, Youssef Rjeb, Asma Ben Tradacete, Pedro |
| author_facet | Azouzi, Youssef Rjeb, Asma Ben Tradacete, Pedro |
| contents | We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space $E$, the free Banach lattice $FBL[E]$ has the strong Nakano property with a constant independent of the dimension. It is also shown that if $FBL[E]$ has the strong Nakano property, then $E$ cannot contain subspaces isomorphic to neither $c_0$ nor $L_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The strong Nakano property in Banach lattices Azouzi, Youssef Rjeb, Asma Ben Tradacete, Pedro Functional Analysis 46B42 We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space $E$, the free Banach lattice $FBL[E]$ has the strong Nakano property with a constant independent of the dimension. It is also shown that if $FBL[E]$ has the strong Nakano property, then $E$ cannot contain subspaces isomorphic to neither $c_0$ nor $L_1$. |
| title | The strong Nakano property in Banach lattices |
| topic | Functional Analysis 46B42 |
| url | https://arxiv.org/abs/2401.15629 |