Lattice isomorphic Banach lattices of polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915769233702912 |
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| author | Boyd, Christopher Miranda, Vinícius |
| author_facet | Boyd, Christopher Miranda, Vinícius |
| contents | We study Díaz-Dineen's problem for regular homogeneous vector-valued polynomials. In particular, we prove that if $E^*$ and $F^*$ are lattice isomorphic
with at least one having order continuous norm, then $\mathcal{P}^r(^n E;
G^*)$ and $\mathcal{P}^r(^n F; G^*)$ are lattice isomorphic for every $n\in
\N$ and every Banach lattice $G$. We also study
the analogous problem for the classes of regular
compact, regular weakly compact, orthogonally additive
and regular nuclear polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lattice isomorphic Banach lattices of polynomials Boyd, Christopher Miranda, Vinícius Functional Analysis We study Díaz-Dineen's problem for regular homogeneous vector-valued polynomials. In particular, we prove that if $E^*$ and $F^*$ are lattice isomorphic with at least one having order continuous norm, then $\mathcal{P}^r(^n E; G^*)$ and $\mathcal{P}^r(^n F; G^*)$ are lattice isomorphic for every $n\in \N$ and every Banach lattice $G$. We also study the analogous problem for the classes of regular compact, regular weakly compact, orthogonally additive and regular nuclear polynomials. |
| title | Lattice isomorphic Banach lattices of polynomials |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.12417 |