The symmetric Radon-Nikodỳm property for tensor norms
We introduce the symmetric Radon-Nikodỳm property (sRN property) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN property, then for every Asplund space E, the ca...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_0022247X_v375_n2_p553_Carando |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v375_n2_p553_Carando |
| Access Level: | acceso abierto |
| Palabra clave: | Metric theory of tensor products Polynomial ideals Radon-Nikodỳm property |
| Sumario: | We introduce the symmetric Radon-Nikodỳm property (sRN property) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN property, then for every Asplund space E, the canonical mapping {position indicator}~βn,sE'→({position indicator}~β'n,sE)' is a metric surjection. This can be rephrased as the isometric isomorphism Qmin(E)=Q(E) for some polynomial ideal Q. We also relate the sRN property of an s-tensor norm with the Asplund or Radon-Nikodỳm properties of different tensor products. As an application, results concerning the ideal of n-homogeneous extendible polynomials are obtained, as well as a new proof of the well-known isometric isomorphism between nuclear and integral polynomials on Asplund spaces. An analogous study is carried out for full tensor products. © 2010 Elsevier Inc. |
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