Journal of Operator Theory

Volume 68, Issue 1, Summer 2012 pp. 205-222.

Maurey-Rosenthal factorization for $p$-summing operators and Dodds-Fremlin domination

Authors: Carlos Palazuelos (1), Enrique A. Sanchez Perez (2), and Pedro Tradacete (3)
Author institution: (1) Departamento de Analisis Matematico Universidad Complutense de Madrid 28040 Madrid, Spain
(2) Instituto Universitario de Matematica Pura y Aplicada Universidad Politecnica de Valencia 46022 Valencia, Spain
(3) Departamento de Matematica Aplicada y Analisis Universidad de Barcelona 08007 Barcelona, Spain

Summary: We characterize by means of a vector norm inequality the space of operators that factorize through a $p$-summing operator from an $L_r$-space to an $L_s$-space. As an application, we prove a domination result in the sense of Dodds-Fremlin for $p$-summing operators on Banach lattices with cotype 2, showing moreover that this cannot hold in general for spaces with higher cotype. We also present a new characterization of Banach lattices satisfying a lower 2-estimate in terms of the order properties of 2-summing operators.

Keywords: $p$-summing operator, positive operator, Banach lattice, factorization, Dodds-Fremlin domination

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