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http://hdl.handle.net/10662/15642
Title: | On operators that preserve the Radon-Nikodým propertys |
Authors: | González Ortiz, Manuel Martínez Abejón, Antonio Pello García, Javier |
Keywords: | Espacio de Banach;Propiedad de Radon-Nikodým;Espacio de Asplund;Espacio ℒ₁;Perturbación compacta;Banach space;Radon-Nikodým property;Asplund space;ℒ₁-space;Compact perturbation |
Issue Date: | 2007 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | We consider a certain class ℛ𝒩+ of operators that preserve the Radon-Nikodým property. Conjugate operators in ℛ𝒩 + can be characterized as those operators 𝑇 such that the kernel 𝑁(𝑇*+K*) has the Radon-Nikodým property for every compact operator K. A construction by J. Bourgain involving infinite convolution products of measures in the Cantor group provides examples of operators 𝑇 : L₁ → L₁ in the class ℛ𝒩 +. As an application, we show the existence of Banach spaces which are ℒ₁-spaces, have the Radon- Nikodým property and contain infinite-dimensional reflexive subspaces. |
URI: | http://hdl.handle.net/10662/15642 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 22, nº 2 (2007) |
Files in This Item:
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2605-5686_22_2_191.pdf | 147,78 kB | Adobe PDF | View/Open |
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