Hardcover ISBN:  9780821808351 
Product Code:  COLL/48 
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eBook ISBN:  9781470431945 
Product Code:  COLL/48.E 
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Hardcover ISBN:  9780821808351 
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Product Code:  COLL/48.B 
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Hardcover ISBN:  9780821808351 
Product Code:  COLL/48 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470431945 
Product Code:  COLL/48.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Hardcover ISBN:  9780821808351 
eBook ISBN:  9781470431945 
Product Code:  COLL/48.B 
List Price:  $168.00 $133.50 
MAA Member Price:  $151.20 $120.15 
AMS Member Price:  $134.40 $106.80 

Book DetailsColloquium PublicationsVolume: 48; 2000; 488 ppMSC: Primary 46; Secondary 22; 28; 47; 52; 54
The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory.
The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories.
Many recent rather deep theorems and delicate examples are included with complete and detailed proofs. Challenging open problems are described and explained, and promising new research directions are indicated.
ReadershipGraduate students and research mathematicians interested in functional analysis; theoretical computer scientists.

Table of Contents

Chapters

Introduction

Chapter 1. Retractions, extensions and selections

Chapter 2. Retractions, extensions and selections (special topics)

Chapter 3. Fixed points

Chapter 4. Differentiation of convex functions

Chapter 5. The RadonNikodým property

Chapter 6. Negligible sets and Gâteaux differentiability

Chapter 7. Lipschitz classification of Banach spaces

Chapter 8. Uniform embeddings into Hilbert space

Chapter 9. Uniform classification of spheres

Chapter 10. Uniform classification of Banach spaces

Chapter 11. Nonlinear quotient maps

Chapter 12. Oscillation of uniformly continuous functions on unit spheres of finitedimensional subspaces

Chapter 13. Oscillation of uniformly continuous functions on unit spheres of infinitedimensional subspaces

Chapter 14. Perturbations of local isometries

Chapter 15. Perturbations of global isometries

Chapter 16. Twisted sums

Chapter 17. Group structure on Banach spaces

Appendices


Additional Material

Reviews

Important monograph, written by leading specialists in the field ... notes and remarks ... contain interesting historical notes and information about a vast amount of related results ... Challenging open problems are described and explained. The vast majority of the material appears for the first time in book form, and many quite recent deep results are proved.
European Mathematical Society Newsletter 
Much ... is explained in this book in a splendid and fascinating way. The considerable amount of mathematics is divided into seventeen chapters which are essentially independent. Three or four of them chosen adlibitum would provide an excellent basis for a graduate course ... researchers will enjoy this invitation to the deepest parts of functional analysis.
Mathematical Reviews 
Without any doubt, this is one of the great books on nonlinear analysis which will certainly become a standard reference. It is not only a must for every math library all over the world, but also for all researchers interested in functional analysis, operator theory, geometry of Banach spaces, and nonlinear problems.
Zentralblatt MATH


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The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory.
The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories.
Many recent rather deep theorems and delicate examples are included with complete and detailed proofs. Challenging open problems are described and explained, and promising new research directions are indicated.
Graduate students and research mathematicians interested in functional analysis; theoretical computer scientists.

Chapters

Introduction

Chapter 1. Retractions, extensions and selections

Chapter 2. Retractions, extensions and selections (special topics)

Chapter 3. Fixed points

Chapter 4. Differentiation of convex functions

Chapter 5. The RadonNikodým property

Chapter 6. Negligible sets and Gâteaux differentiability

Chapter 7. Lipschitz classification of Banach spaces

Chapter 8. Uniform embeddings into Hilbert space

Chapter 9. Uniform classification of spheres

Chapter 10. Uniform classification of Banach spaces

Chapter 11. Nonlinear quotient maps

Chapter 12. Oscillation of uniformly continuous functions on unit spheres of finitedimensional subspaces

Chapter 13. Oscillation of uniformly continuous functions on unit spheres of infinitedimensional subspaces

Chapter 14. Perturbations of local isometries

Chapter 15. Perturbations of global isometries

Chapter 16. Twisted sums

Chapter 17. Group structure on Banach spaces

Appendices

Important monograph, written by leading specialists in the field ... notes and remarks ... contain interesting historical notes and information about a vast amount of related results ... Challenging open problems are described and explained. The vast majority of the material appears for the first time in book form, and many quite recent deep results are proved.
European Mathematical Society Newsletter 
Much ... is explained in this book in a splendid and fascinating way. The considerable amount of mathematics is divided into seventeen chapters which are essentially independent. Three or four of them chosen adlibitum would provide an excellent basis for a graduate course ... researchers will enjoy this invitation to the deepest parts of functional analysis.
Mathematical Reviews 
Without any doubt, this is one of the great books on nonlinear analysis which will certainly become a standard reference. It is not only a must for every math library all over the world, but also for all researchers interested in functional analysis, operator theory, geometry of Banach spaces, and nonlinear problems.
Zentralblatt MATH