A nonlinear transfer technique for renorming
Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem....
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| Auteurs principaux: | , , , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2009. |
| Collection: | Lecture Notes in Mathematics
1951 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Description d'apès consultation du 23 janvier 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • A nonlinear transfer technique for renorming, Aníbal Moltó, José Orihuela, Stanimir Troyanski [et al.], Berlin, Springer, 2009, 1 vol. (XI-142 p.), Lecture notes in mathematics, 978-3-540-85030-4 • A Nonlinear Transfer Technique for Renorming, Texte imprimé, 9783540872986 • A nonlinear transfer technique for renorming, Aníbal Moltó, José Orihuela, Stanimir Troyanski [et al.], Berlin, Springer, 2009, 1 vol. (XI-142 p.), Lecture notes in mathematics, 978-3-540-85030-4 |
| Résumé: | Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis. |
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| Description: | Description d'apès consultation du 23 janvier 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783540850311 |
| ISSN: | 1617-9692 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |