Maurey-Rosenthal factorization of positive operators and convexity |
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| Authors: | A. Defant,E.A. Sá nchez Pé rez |
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| Affiliation: | a Faculty V, Institute of Mathematics, University of Oldenburg, D-26111 Oldenburg, Germany
b ETSI Caminos, Canales y Puertos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain |
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| Abstract: | We show that a Banach lattice X is r-convex, 1<r<∞, if and only if all positive operators T on X with values in some r-concave Köthe function spaces F(ν) (over measure spaces (Ω,ν)) factorize strongly through Lr(ν) (i.e., T=MgR, where R is an operator from X to Lr(ν) and Mg a multiplication operator on Lr(ν) with values in F). This characterization of r-convexity motivates a Maurey-Rosenthal type factorization theory for positive operators acting between vector valued Köthe function spaces. |
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| Keywords: | Positive operator Kö the function space Convexity Concavity |
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