Pietsch-Maurey-Rosenthal factorization of summing multilinear operators
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 -spaces. A~by-product of our factorization is an extension of multilinear operators defined by a~-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 -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 -concavity. This class contains -dominated operators, and so the obtained results provide a~new factorization theorem for operators from this class.
Cite
@article{arxiv.1706.06017,
title = {Pietsch-Maurey-Rosenthal factorization of summing multilinear operators},
author = {Mieczysław Mastyło and Enrique A. Sánchez-Pérez},
journal= {arXiv preprint arXiv:1706.06017},
year = {2017}
}