Overview

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.

Full Product Details

9783540850304

Table of Contents

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)

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available