A generalization of p-convexity and q-concavity on Banach lattices
Abstract
In this paper, considering a real Banach sequence lattice Y instead of a Lebesgue sequence space lp 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.
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