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arXiv · 2311.01124

A generalization of p-convexity and q-concavity on Banach lattices

Fernando Galaz-Fontes·José Luis Hernández-Barradas
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Abstract

In this paper, considering a real Banach sequence lattice Y instead of a Lebesgue sequence space $l_p$ we generalize p-convexity of a linear operator $T:E\to X$, where E is a Banach space and X is a Banach lattice. Then we prove that basic properties of p-convexity remain valid for Y-convex linear operators. Analogous generalizations are given for q-concavity and p-summability and composition properties between these operators are analyzed.

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Fernando Galaz-Fontes, José Luis Hernández-Barradas. 2023-11-02. A generalization of p-convexity and q-concavity on Banach lattices. https://arxiv.org/abs/2311.01124

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