Banach lattices of positively homogeneous functions induced by a Banach space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915726839775232 |
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| author | Laustsen, Niels Jakob Tradacete, Pedro |
| author_facet | Laustsen, Niels Jakob Tradacete, Pedro |
| contents | Motivated by the construction of the free Banach lattice generated by a Banach space, we introduce and study several vector and Banach lattices of positively homogeneous functions defined on the dual of a Banach space $E$. The relations between these lattices allow us to give multiple characterizations of when the underlying Banach space $E$ is finite-dimensional and when it is reflexive. Furthermore, we show that lattice homomorphisms between free Banach lattices are always composition operators, and study how these operators behave on the scale of lattices of positively homogeneous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Banach lattices of positively homogeneous functions induced by a Banach space Laustsen, Niels Jakob Tradacete, Pedro Functional Analysis 46B42, 46E05, 46B50 Motivated by the construction of the free Banach lattice generated by a Banach space, we introduce and study several vector and Banach lattices of positively homogeneous functions defined on the dual of a Banach space $E$. The relations between these lattices allow us to give multiple characterizations of when the underlying Banach space $E$ is finite-dimensional and when it is reflexive. Furthermore, we show that lattice homomorphisms between free Banach lattices are always composition operators, and study how these operators behave on the scale of lattices of positively homogeneous functions. |
| title | Banach lattices of positively homogeneous functions induced by a Banach space |
| topic | Functional Analysis 46B42, 46E05, 46B50 |
| url | https://arxiv.org/abs/2404.06497 |