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

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Palazuelos Cabezón, Carlos and Sánchez Pérez, Enrique A. and Tradacete Pérez, Pedro (2012) Maurey-Rosenthal factorization for p-summing operators and Dodds-Fremlin domination. Journal of operator theory, 68 (1). pp. 205-222. ISSN 1841-7744

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Official URL: http://www.mathjournals.org/jot/2012-068-001/2012-068-001-011.pdf


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:p-summing operator; positive operator; Banach lattice; factorization; Dodds-Fremlin domination
Subjects:Sciences > Mathematics
ID Code:24433
Deposited On:30 Jan 2014 10:23
Last Modified:03 Apr 2019 16:25

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