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

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.