On the free Banach lattice generated by a lattice
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915970777350144 |
|---|---|
| author | Rjeb, Asma Ben Tradacete, Pedro |
| author_facet | Rjeb, Asma Ben Tradacete, Pedro |
| contents | We study structural properties of the free Banach lattice $FBL\langle L\rangle$ generated by a distributive lattice $L$. We characterize when $FBL\langle L\rangle$ has a strong unit, compute its density character, analyze the density character of order intervals and study when is $FVL\langle L\rangle$ order dense in $FBL\langle L\rangle$. We also study projection bands, quasi-interior points, and Banach lattice homomorphisms induced by lattice homomorphisms. Finally, we show that $FBL\langle L\rangle$ is lattice isometric to $FBL\langle L^{\mathrm{op}}\rangle$, where $L^{\mathrm{op}}$ denotes the opposite lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the free Banach lattice generated by a lattice Rjeb, Asma Ben Tradacete, Pedro Functional Analysis 46B42, 06B05 We study structural properties of the free Banach lattice $FBL\langle L\rangle$ generated by a distributive lattice $L$. We characterize when $FBL\langle L\rangle$ has a strong unit, compute its density character, analyze the density character of order intervals and study when is $FVL\langle L\rangle$ order dense in $FBL\langle L\rangle$. We also study projection bands, quasi-interior points, and Banach lattice homomorphisms induced by lattice homomorphisms. Finally, we show that $FBL\langle L\rangle$ is lattice isometric to $FBL\langle L^{\mathrm{op}}\rangle$, where $L^{\mathrm{op}}$ denotes the opposite lattice. |
| title | On the free Banach lattice generated by a lattice |
| topic | Functional Analysis 46B42, 06B05 |
| url | https://arxiv.org/abs/2604.27841 |