Arens extensions of disjointness preserving multilinear operators on Riesz spaces and Banach lattices
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911274897506304 |
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| author | Botelho, Geraldo Garcia, Luis Alberto Miranda, Vinícius C. C. |
| author_facet | Botelho, Geraldo Garcia, Luis Alberto Miranda, Vinícius C. C. |
| contents | Let $E_1, \ldots, E_m$ be (non necessarily Archimedean) Riesz spaces, let $F$ be an Archimedean Riesz space and let $A \colon E_1 \times \cdots \times E_m \to F$ be a regular disjointness preserving $m$-linear operator. We prove that all Arens extensions of $A$ are disjointness preserving if either $A$ has finite lattice rank or the spaces are Banach lattices and $F^*$ has a Schauder basis consisting of disjointness preserving functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arens extensions of disjointness preserving multilinear operators on Riesz spaces and Banach lattices Botelho, Geraldo Garcia, Luis Alberto Miranda, Vinícius C. C. Functional Analysis 46A40, 46B24, 46G25, 47H60 Let $E_1, \ldots, E_m$ be (non necessarily Archimedean) Riesz spaces, let $F$ be an Archimedean Riesz space and let $A \colon E_1 \times \cdots \times E_m \to F$ be a regular disjointness preserving $m$-linear operator. We prove that all Arens extensions of $A$ are disjointness preserving if either $A$ has finite lattice rank or the spaces are Banach lattices and $F^*$ has a Schauder basis consisting of disjointness preserving functionals. |
| title | Arens extensions of disjointness preserving multilinear operators on Riesz spaces and Banach lattices |
| topic | Functional Analysis 46A40, 46B24, 46G25, 47H60 |
| url | https://arxiv.org/abs/2502.21103 |