Pietsch-Maurey-Rosenthal factorization of summing multilinear operators

2017/06/19 by Mastyło, Mieczysław, Sánchez-Pérez, Enrique A.
#46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1706.06017

Abstract

The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for these operators is proved under weaker convexity requirements than the ones that are needed in the Maurey-Rosenthal factorization through products of L^q-spaces. A~by-product of our factorization is an extension of multilinear operators defined by a~q-concavity type property to a~product of special Banach function lattices which inherit some lattice-geometric properties of the domain spaces, as order continuity and p-convexity. Factorization through Fremlin's tensor products is also analyzed. Applications are presented to study a~special class of linear operators between Banach function lattices that can be characterized by a strong version of q-concavity. This class contains q-dominated operators, and so the obtained results provide a~new factorization theorem for operators from this class.

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