Smoothness and Renormings in Banach Spaces - Couverture rigide

Couverture rigide

ISBN 10 : 0470220880 ISBN 13 : 9780470220887

Synopsis

The purpose of this book is to provide the reader with a self-contained treatment of the basic techniques of construction of equivalent norms on Banach spaces which enjoy special properties of convexity and smoothness. We also show how the existence of such norms relates to the structure of the space, and provide applications in various directions. Most of the results discussed in this work are less than a decade old. The proofs of some older theorems have also been greatly simplified. The book gives a detailed and up-to-date account of duality results and variational principles. An exploitation of Martingale techniques in the local and in the infinite-dimensional case is given. Rough norms are applied to the "harmonic" behaviour of smooth maps defined on non-smooth spaces, and to Mooney-Havin type theorems. The book also provides a systematic presentation of higher order smoothness and Taylor polynomials on Banach spaces, which leads to the construction of lp-subspaces.

The structure of non-seperable spaces which satisfy a "countability condition" is elucidated through the use of long sequences of projections, and a unified way of constructing locally uniformly rotund norms on such spaces is introduced. The authors investigate approximation and perturbation by smooth functions, and applications to viscosity solutions of Hamilton-Jacobi equations in the infinite-dimensional case. A list of annotated open problems concludes each section. This book will be of interest to graduate students and researchers working in Banach space theory, optimization, differential equations and related areas of functional analysis. A basic knowledge of functional analysis is assumed.

À propos de cette édition

• ISBN 10: 0470220880
• ISBN 13: 9780470220887
• Reliure: Hardcover