Renormings In Banach Spaces

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Renormings In Banach Spaces

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Author : Antonio José Guirao
language : en
Publisher: Springer Nature
Release Date : 2022-08-23

Renormings In Banach Spaces written by Antonio José Guirao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.

This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.

Smoothness And Renormings In Banach Spaces

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Author : Robert Deville
language : en
Publisher: Chapman & Hall/CRC
Release Date : 1993

Smoothness And Renormings In Banach Spaces written by Robert Deville and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

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.

A Nonlinear Transfer Technique For Renorming

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Author : Aníbal Moltó
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

A Nonlinear Transfer Technique For Renorming written by Aníbal Moltó and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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.

Renormings In Banach Spaces

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Author : Antonio J. Guirao
language : en
Publisher:
Release Date : 2022

Renormings In Banach Spaces written by Antonio J. Guirao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Banach spaces categories.

This monograph is devoted to the study of Eulerian models for fluid-structure interaction from the original point of view of level set methods. In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction problems. One major advantage compared to more conventional methods such as ALE methods is that they allow the use of a single grid and a single discretization method for the different media. Level set methods in addition provide a general framework to follow the fluid-solid interfaces, to represent the elastic stresses of solids, and to model the contact forces between solids. This book offers a combination of mathematical modeling, aspects of numerical analysis, elementary codes and numerical illustrations, providing the reader with insights into the applications and performance of these models. Assuming background at the level of a Master’s degree, Level Set Methods for Fluid-Structure Interaction provides researchers in the fields of numerical analysis of PDEs, theoretical and computational mechanics with a basic reference on the topic. Its pedagogical style and organization make it particularly suitable for graduate students and young researchers.

Biorthogonal Systems In Banach Spaces

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Author : Petr Hajek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-04

Biorthogonal Systems In Banach Spaces written by Petr Hajek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-04 with Mathematics categories.

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

Open Problems In The Geometry And Analysis Of Banach Spaces

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Author : Antonio J. Guirao
language : en
Publisher: Springer
Release Date : 2016-07-26

Open Problems In The Geometry And Analysis Of Banach Spaces written by Antonio J. Guirao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-26 with Mathematics categories.

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.

Geometry Of Banach Spaces Selected Topics

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Author : J. Diestel
language : en
Publisher: Springer
Release Date : 2006-11-14

Geometry Of Banach Spaces Selected Topics written by J. Diestel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Fixed Point Property Under Renormings In Non Reflexive Banach Spaces

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Author : Carlos Alberto Hernández Linares
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012-07

Fixed Point Property Under Renormings In Non Reflexive Banach Spaces written by Carlos Alberto Hernández Linares and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07 with categories.

Consider a subset C of a Banach space (X, .). Let T be a mapping from a set C to itself, it is said that a point x in C is a fixed point for T if Tx=x. This mapping is a nonexpansive mapping if Tx - Ty x - y for all x and y belonging to C. It is said that a Banach space X has the fixed point property (FPP) if every nonexpansive mapping defined from a closed convex bounded subset into itself has a fixed point. For a long time, it was conjectured that all Banach spaces with the FPP had to be reflexive. In 2008, it was given an unexpected answer to this conjecture: it was found the first known nonreflexive Banach space with the FPP. On the other hand, in 2009, it was proved that every reflexive Banach space can be renormed to have the FPP. This leads us to the following question: Which type of nonreflexive Banach spaces can be renormed to have the FPP? So, the main object of this book is to study new families of nonreflexive Banach spaces which can be renormed to have the FPP

Renorming And Smoothness In Banach Spaces

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Author : Jon Dwight Vanderwerff
language : en
Publisher:
Release Date : 1992

Renorming And Smoothness In Banach Spaces written by Jon Dwight Vanderwerff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.

Classical Banach Spaces Ii

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Author : J. Lindenstrauss
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

Classical Banach Spaces Ii written by J. Lindenstrauss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.