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Journal of Convex Analysis 20 (2013), No. 4, 999--1012
Copyright Heldermann Verlag 2013

Domination and Factorization of Multilinear Operators

Mieczyslaw Mastylo
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland

Enrique A. Sánchez Pérez
Instituto de Matemática Pura y Aplicada, Universidad Politécnica, Camino de Vera s/n, 46022 Valencia, Spain

We study multilinear operators from quasi-Banach lattices to quasi-Banach spaces. We prove that certain vector valued norm inequalities for these operators are equivalent to domination theorems. As an application we show that under some mild assumptions these domination theorems can be expressed in terms of factorization through Orlicz spaces. In the case of the multilinear functionals on C(K)-spaces we recover a multilinear variant of the Grothendieck factorization theorem.

Keywords: Factorization, Banach function lattice, Banach envelope, Orlicz space.

MSC: 46E30; 47B38, 46B42

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