ENGLISH

A nonlinear transfer technique for renorming

By Aníbal Moltó , José Orihuela , Stanimir Troyanski , Manuel Valdivia (eds.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3540850309, 9783540850304
DOI
10.1007/978-3-540-85031-1
Language
english
Format
PDF
Filesize
1 MB (1380510 bytes)
Series
Lecture Notes in Mathematics 1951
Edition
1
Pages
148\153
Library
Kolxo3
Time added
2009-07-20 03:45:11
Functional Analysis; Differential Geometry

Description

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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2010 · PDF