Duality between Y-convexity and Y^×-concavity of linear operators between Banach lattices

2024/05/30 by Hernández-Barradas, José Luis, Galaz-Fontes, Fernando
#46B42 #47A30 #47B10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.19579

Abstract

In this paper we study the Y-convexity, a property which is obtained by considering a real Banach sequence lattice Y instead of ℓ^p for a linear operator T : E → 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 T. Analogous results for Y-concavity are also obtained. Finally, the duality between Y-convexity and Y^×-concavity is proven.

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