The symmetric Radon-Nikodým property for tensor norms
We introduce the symmetric-Radon-Nikodým property (sRN pr operty) 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 prop- erty, then for every Asplund space E , th...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/14933 |
| Acesso em linha: | http://hdl.handle.net/11336/14933 |
| Access Level: | acceso abierto |
| Palavra-chave: | Polynomial ideals Symmetric tensor products of Banach spaces Radon-Nikodým property https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We introduce the symmetric-Radon-Nikodým property (sRN pr operty) 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 prop- erty, then for every Asplund space E , the canonical map e ⊗ n,s β E ′ → e ⊗ n,s β ′ E ′ is a metric surjection. This can be rephrased as the isometric isomorph ism Q min ( E ) = Q ( E ) for certain polynomial ideal Q . We also relate the sRN property of an s-tensor norm with the A splund or Radon-Nikodým properties of different tensor products. S imilar results for full tensor products are also given. As an application, results concern ing the ideal of n -homogeneous extendible polynomials are obtained, as well as a new proof o f the well known isometric isomorphism between nuclear and integral polynomials on As plund spaces. |
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