Duality between Y-convexity and $Y^{\times}$-concavity of linear operators between Banach lattices
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| Format: | Preprint |
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2024
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| author | Hernández-Barradas, José Luis Galaz-Fontes, Fernando |
| author_facet | Hernández-Barradas, José Luis Galaz-Fontes, Fernando |
| contents | In this paper we study the Y-convexity, a property which is obtained by considering a real Banach sequence lattice Y instead of $\ell^p$ for a linear operator $T : E \rightarrow X$, where E is a Banach space and X is a Banach lattice. We introduce some vector sequence spaces in order to characterize the Y-convexity of T by means of the continuity of an associated operator $\overline{T}$. Analogous results for Y-concavity are also obtained. Finally, the duality between Y-convexity and $Y^{\times}$-concavity is proven. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19579 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality between Y-convexity and $Y^{\times}$-concavity of linear operators between Banach lattices Hernández-Barradas, José Luis Galaz-Fontes, Fernando Functional Analysis 46B42, 47A30, 47B10 In this paper we study the Y-convexity, a property which is obtained by considering a real Banach sequence lattice Y instead of $\ell^p$ for a linear operator $T : E \rightarrow X$, where E is a Banach space and X is a Banach lattice. We introduce some vector sequence spaces in order to characterize the Y-convexity of T by means of the continuity of an associated operator $\overline{T}$. Analogous results for Y-concavity are also obtained. Finally, the duality between Y-convexity and $Y^{\times}$-concavity is proven. |
| title | Duality between Y-convexity and $Y^{\times}$-concavity of linear operators between Banach lattices |
| topic | Functional Analysis 46B42, 47A30, 47B10 |
| url | https://arxiv.org/abs/2405.19579 |