Functiones et Approximatio Commentarii Mathematici

Pietsch--Maurey--Rosenthal factorization of summing multilinear operators

Mieczysław Mastyło and Enrique A. Sánchez Pérez

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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.

Article information

Funct. Approx. Comment. Math., Volume 59, Number 1 (2018), 57-76.

First available in Project Euclid: 28 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 47B38: Operators on function spaces (general) 46B42: Banach lattices [See also 46A40, 46B40]

extension summing multilinear operator factorization $p$-convex Banach lattice


Mastyło, Mieczysław; Pérez, Enrique A. Sánchez. Pietsch--Maurey--Rosenthal factorization of summing multilinear operators. Funct. Approx. Comment. Math. 59 (2018), no. 1, 57--76. doi:10.7169/facm/1683.

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