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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1951)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
From the reviews:
“The purpose of this monograph is to present a new general framework for the study of locally uniformly rotund (LUR) renormings. … In this monograph the authors give a complete description of an important and new general framework. This is certainly a very valuable up-to-date reference for specialists in renorming theory. It is also accessible to young researchers willing to discover this domain … .” (Gilles Lancien, Mathematical Reviews, Issue 2010 a)
“The authors of the book under review, contributed a lot to the progress achieved in renorming theory over the last fifteen years. … This nice and deep book addresses problems which are of interest for every functional analyst, and, moreover, anyone who intends to contribute to renorming theory must read it. I should finally mention that a very interesting list of commented problems concludes the book. This list constitutes an attractive research program, which should stimulate research for the years to come.” (Gilles Godefroy, Zentralblatt MATH, Vol. 1182, 2010)
Authors and Affiliations
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Departamento de Análisis Matemático Facultad de Matemáticas, Universidad de Valencia, Burjasot, Valencia, Spain
Aníbal Moltó, Manuel Valdivia
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Departamento de Matemáticas, Universidad de Murcia, Murcia, Spain
José Orihuela, Stanimir Troyanski
Bibliographic Information
Book Title: A Nonlinear Transfer Technique for Renorming
Authors: Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-85031-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-540-85030-4Published: 21 October 2008
eBook ISBN: 978-3-540-85031-1Published: 15 October 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XI, 148
Topics: Differential Geometry, Functional Analysis