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arXiv · 2405.19579

Duality between Y-convexity and $Y^{\times}$-concavity of linear operators between Banach lattices

José Luis Hernández-Barradas·Fernando Galaz-Fontes
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Abstract

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.

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José Luis Hernández-Barradas, Fernando Galaz-Fontes. 2024-05-30. Duality between Y-convexity and $Y^{\times}$-concavity of linear operators between Banach lattices. https://arxiv.org/abs/2405.19579

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