Geometric nonlinear functional analysis
Author(s)
Bibliographic Information
Geometric nonlinear functional analysis
（Colloquium publications / American Mathematical Society, v. 48）
American Mathematical Society, c2000
- v. 1
Available at / 49 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
v. 1BEN||38||199086887
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
v. 1515.7/B4482070496273
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
Introduction Retractions, extensions and selections Retractions, extensions and selections (special topics) Fixed points Differentiation of convex functions The Radon-Nikodym property Negligible sets and Gateaux differentiability Lipschitz classification of Banach spaces Uniform embeddings into Hilbert space Uniform classification of spheres Uniform classification of Banach spaces Nonlinear quotient maps Oscillation of uniformly continuous functions on unit spheres of finite-dimensional subspaces Oscillation of uniformly continuous functions on unit spheres of infinite-dimensional subspaces Perturbations of local isometries Perturbations of global isometries Twisted sums Group structure on Banach spaces Appendices Bibliography Index.
by "Nielsen BookData"