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

Fernando Galaz-Fontes, José Luis Hernández-Barradas

Published 2023-11-02Version 1

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.