A Nonlinear Transfer Technique for Renorming

2009
ISBN: 978-3-540-85030-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1951, 148 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g

Reihe: Lecture Notes in Mathematics

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 c 0 (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.

Zielgruppe

Research

Autoren/Hrsg.

Moltó, Aníbal

Valdivia, Manuel

Orihuela, José

Troyanski, Stanimir

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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