عنوان

A nonlinear transfer technique for renorming

(Number (ISBN

9783540850304 (pbk.)

Country Code

IR

Number

10720

.Language of Text, Soundtrack etc

انگلیسی

Country of publication

IR

Title Proper

A nonlinear transfer technique for renorming

General Material Designation

[Book]

First Statement of Responsibility

/ Aniلإbal Moltoلإ ... [et al.].

Specific Material Designation and Extent of Item

xi, 142 p. ; 24 cm.

Series Title

(Lecture notes in mathematics 0075-8434

Volume Designation

; 1951)

Text of Note

Language: انگلیسی

Text of Note

Print

Text of Note

Includes bibliographical references and index.

Text of Note

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 Frechet 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.Review: 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)

Metric spaces.

Continuum (Mathematics)

Mappings (Mathematics)

Banach spaces.

Class number

Book number

Moltoلإ, Aniلإbal

Country

ایران

old catalog

p

BL

1

a

Y