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September 2018 Pietsch--Maurey--Rosenthal factorization of summing multilinear operators
Mieczysław Mastyło, Enrique A. Sánchez Pérez
Funct. Approx. Comment. Math. 59(1): 57-76 (September 2018). DOI: 10.7169/facm/1683


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 anew factorization theorem for operators from this class.


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Mieczysław Mastyło. Enrique A. Sánchez Pérez. "Pietsch--Maurey--Rosenthal factorization of summing multilinear operators." Funct. Approx. Comment. Math. 59 (1) 57 - 76, September 2018.


Published: September 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06979909
MathSciNet: MR3858279
Digital Object Identifier: 10.7169/facm/1683

Primary: 46E30
Secondary: 46B42 , 47B38

Keywords: $p$-convex , Banach lattice , Extension‎ , factorization , summing multilinear operator

Rights: Copyright © 2018 Adam Mickiewicz University

Vol.59 • No. 1 • September 2018
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