Vector measure range duality and factorizations of (D, p)-summing operators from Banach function spaces

Abstract.

We characterize the relationship between the space L ₁(λ’) and the dual L’₁(λ) of the space L ₁(λ), where (λ, λ’) is a dual pair of vector measures with associated spaces of integrable functions L ₁(λ) and L ₁(λ’) respectively. Since the result is rather restrictive, we introduce the notion of range duality in order to obtain factorizations of operators from Banach function spaces that are dominated by the integration map associated to the vector measure λ. We obtain in this way a generalization of the Grothendieck-Pietsch Theorem for p-summing operators.