A Nonlinear Transfer Technique for Renorming

Buch | Softcover
XI, 148 Seiten
2008 | 2009
Springer Berlin (Verlag)
978-3-540-85030-4 (ISBN)

Lese- und Medienproben

A Nonlinear Transfer Technique for Renorming - Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia
37,40 inkl. MwSt
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.

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.

?-Continuous and Co-?-continuous Maps.- Generalized Metric Spaces and Locally Uniformly Rotund Renormings.- ?-Slicely Continuous Maps.- Some Applications.- Some Open Problems.

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)

Erscheint lt. Verlag 21.10.2008
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XI, 148 p.
Verlagsort Berlin
Sprache englisch
Gewicht 259 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte 46B03, 46B20, 46B26, 46T20, 54D620, 54E18, 54E25, 54E35 • Banach space • Banach spaces • Convexity • Functional Analysis • metrizability • Networks • Renorming
ISBN-10 3-540-85030-9 / 3540850309
ISBN-13 978-3-540-85030-4 / 9783540850304
Zustand Neuware
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