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# 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)
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.