| Hardcover ISBN: | 978-0-8218-0835-1 |
| Product Code: | COLL/48 |
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| eBook ISBN: | 978-1-4704-3194-5 |
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| AMS Member Price: | $55.20 |
| Hardcover ISBN: | 978-0-8218-0835-1 |
| eBook: ISBN: | 978-1-4704-3194-5 |
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| AMS Member Price: | $134.40 $106.80 |
| Hardcover ISBN: | 978-0-8218-0835-1 |
| Product Code: | COLL/48 |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-3194-5 |
| Product Code: | COLL/48.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| Hardcover ISBN: | 978-0-8218-0835-1 |
| eBook ISBN: | 978-1-4704-3194-5 |
| 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 |
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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.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. Retractions, extensions and selections
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Chapter 2. Retractions, extensions and selections (special topics)
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Chapter 3. Fixed points
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Chapter 4. Differentiation of convex functions
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Chapter 5. The Radon-Nikodým property
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Chapter 6. Negligible sets and Gâteaux differentiability
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Chapter 7. Lipschitz classification of Banach spaces
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Chapter 8. Uniform embeddings into Hilbert space
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Chapter 9. Uniform classification of spheres
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Chapter 10. Uniform classification of Banach spaces
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Chapter 11. Nonlinear quotient maps
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Chapter 12. Oscillation of uniformly continuous functions on unit spheres of finite-dimensional subspaces
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Chapter 13. Oscillation of uniformly continuous functions on unit spheres of infinite-dimensional subspaces
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Chapter 14. Perturbations of local isometries
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Chapter 15. Perturbations of global isometries
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Chapter 16. Twisted sums
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Chapter 17. Group structure on Banach spaces
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Appendices
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Additional Material
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Reviews
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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 ad-libitum 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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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 Radon-Nikodým 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 finite-dimensional subspaces
-
Chapter 13. Oscillation of uniformly continuous functions on unit spheres of infinite-dimensional 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 ad-libitum 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
