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| Softcover ISBN: | 978-1-4704-7347-1 |
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| Softcover ISBN: | 978-1-4704-7347-1 |
| Product Code: | ULECT/79 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-7879-7 |
| Product Code: | ULECT/79.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-1-4704-7347-1 |
| eBook ISBN: | 978-1-4704-7879-7 |
| Product Code: | ULECT/79.B |
| List Price: | $134.00 $101.50 |
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Book DetailsUniversity Lecture SeriesVolume: 79; 2024; Estimated: 268 ppMSC: Primary 46
The main theme of the book is the nonlinear geometry of Banach spaces, and it considers various significant problems in the field. The present book is a commented transcript of the notes of the graduate-level topics course in nonlinear functional analysis given by the late Nigel Kalton in 2008.
Nonlinear geometry of Banach spaces is a very active area of research with connections to theoretical computer science, noncommutative geometry, as well as geometric group theory and Nigel Kalton was the most influential and prolific contributor to the theory. Collected here are the topics that Nigel Kalton felt were significant for those first dipping a toe into the subject of nonlinear functional analysis and presents these topics in an accessible and concise manner. As well as covering some well-known topics, it also includes recent results discovered by Kalton and his collaborators which have not previously appeared in textbook form. A typical first-year course in functional analysis will provide sufficient background for readers of this book.
ReadershipGraduate students and researchers interested in nonlinear geometry of Banach spaces.
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Table of Contents
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Absolute Lipschitz retracts
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Lipschitz extensions and Hilbert spaces
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Convex subsets and selections
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Lipschitz classification of Banach spaces
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Arens-Eells space
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Differentiation and the isomorphism problem
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Differentiation and Haar-null sets
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Property $\Pi (\lambda)$ and embeddings into $c_o$
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Local complementation and the Heinrich-Mankiewicz theorem
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The Lipschitz structure of $c_o$
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Ultraproducts of Banach spaces
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The uniform structure of Banach spaces
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The unique uniform structure of sequence spaces
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Uniform embeddings into a Hilbert space
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Uniform embeddings into reflexive spaces
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Exercises
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Afterword (where to from here)
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Vector integration
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The Radon-Nikodym property
-
Gaussian measures
-
Notes on closest points
-
Bibliography
-
Index
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
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- Requests
The main theme of the book is the nonlinear geometry of Banach spaces, and it considers various significant problems in the field. The present book is a commented transcript of the notes of the graduate-level topics course in nonlinear functional analysis given by the late Nigel Kalton in 2008.
Nonlinear geometry of Banach spaces is a very active area of research with connections to theoretical computer science, noncommutative geometry, as well as geometric group theory and Nigel Kalton was the most influential and prolific contributor to the theory. Collected here are the topics that Nigel Kalton felt were significant for those first dipping a toe into the subject of nonlinear functional analysis and presents these topics in an accessible and concise manner. As well as covering some well-known topics, it also includes recent results discovered by Kalton and his collaborators which have not previously appeared in textbook form. A typical first-year course in functional analysis will provide sufficient background for readers of this book.
Graduate students and researchers interested in nonlinear geometry of Banach spaces.
-
Absolute Lipschitz retracts
-
Lipschitz extensions and Hilbert spaces
-
Convex subsets and selections
-
Lipschitz classification of Banach spaces
-
Arens-Eells space
-
Differentiation and the isomorphism problem
-
Differentiation and Haar-null sets
-
Property $\Pi (\lambda)$ and embeddings into $c_o$
-
Local complementation and the Heinrich-Mankiewicz theorem
-
The Lipschitz structure of $c_o$
-
Ultraproducts of Banach spaces
-
The uniform structure of Banach spaces
-
The unique uniform structure of sequence spaces
-
Uniform embeddings into a Hilbert space
-
Uniform embeddings into reflexive spaces
-
Exercises
-
Afterword (where to from here)
-
Vector integration
-
The Radon-Nikodym property
-
Gaussian measures
-
Notes on closest points
-
Bibliography
-
Index
