Nigel Kalton's Lectures in Nonlinear Functional Analysis
American Mathematical Society (Verlag)
9781470473471 (ISBN)
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.
Adam Bowers, University of California, San Diego, CA
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
| Erscheinungsdatum | 29.01.2025 |
|---|---|
| Reihe/Serie | University Lecture Series |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-13 | 9781470473471 / 9781470473471 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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