Article

Domination spaces and factorization of linear and multilinear summing operators

Published in: Quaestiones Mathematicae
Volume 39 , issue 8 , 2016 , pages: 1071–1092

DOI: 10.2989/16073606.2016.1253627

Author(s): Dahmane Achour Universitáe Mohamed Boudiaf-M’sila, Laboratoire d’Analyse Fonctionnelle et Géeoméetrie des Espaces, Algeria , Elhadj Dahia Universitáe Mohamed Boudiaf-M’sila, Laboratoire d’Analyse Fonctionnelle et Géeoméetrie des Espaces, Algeria , Pilar Rueda Departamento de Ańalisis Matemáatico Universidad de Valencia, Spain , Enrique A. Sánchez-Pérez Instituto Universitario de Matemáatica Pura y Aplicada, Universitat Politèecnica de Valèencia, Spain

Keywords: Primary 47B10 , Secondary 47L22 , 46A32 , Primary 47B10 , Secondary 47L22 , 46A32

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Abstract

It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, σ)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p1, . . . , pn)-dominated multilinear operators and dominated (p1, . . . , pn; σ)-continuous multilinear operators.

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