Free dual spaces and free Banach lattices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909816977358848 |
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| author | García-Sánchez, Enrique Tradacete, Pedro |
| author_facet | García-Sánchez, Enrique Tradacete, Pedro |
| contents | The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space $E$ the free $p$-convex Banach lattice generated by $E^{**}$, denoted $FBL^p[E^{**}]$, admits a canonical isometric lattice embedding into $FBL^p[E]^{**}$ and $FBL^p[E^{**}]$ is lattice finitely representable in $FBL^p[E]$. Moreover, we also show that for $p>1$, $FBL^p[E]^{**}$ can actually be considered as the free dual $p$-convex Banach lattice generated by $E$, whereas for $p=1$ this happens precisely when $E$ does not contain complemented copies of $\ell_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09225 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Free dual spaces and free Banach lattices García-Sánchez, Enrique Tradacete, Pedro Functional Analysis 46B42, 46B10, 46A11 The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space $E$ the free $p$-convex Banach lattice generated by $E^{**}$, denoted $FBL^p[E^{**}]$, admits a canonical isometric lattice embedding into $FBL^p[E]^{**}$ and $FBL^p[E^{**}]$ is lattice finitely representable in $FBL^p[E]$. Moreover, we also show that for $p>1$, $FBL^p[E]^{**}$ can actually be considered as the free dual $p$-convex Banach lattice generated by $E$, whereas for $p=1$ this happens precisely when $E$ does not contain complemented copies of $\ell_1$. |
| title | Free dual spaces and free Banach lattices |
| topic | Functional Analysis 46B42, 46B10, 46A11 |
| url | https://arxiv.org/abs/2210.09225 |