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

2023/11/02 by Fernando Galaz-Fontes, Galaz-Fontes, Fernando, José Luis Hernández-Barradas +1
Computer Science · Mathematics · #46B42 #47A30 #47B10 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2311.01124

openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→ 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.

Related

• Duality between Y-convexity and Y^×-concavity of linear operators between Banach lattices
• Lipschitz p-convex and q-concave maps
• Free Banach lattices under convexity conditions
• Optimal domain of q-concave operators and vector measure representation of q-concave Banach lattices
• Pietsch-Maurey-Rosenthal factorization of summing multilinear operators