Nigel Kalton's lectures in nonlinear functional analysis / Adam Bowers.

Format:

Book

Author/Creator:

Bowers, Adam (Adam Roman), author.

Series:

University lecture series (Providence, R.I.) ; 79.

University lecture series ; volume 79

Language:

English

Subjects (All):

Kalton, Nigel J. (Nigel John), 1946-2010.

Kalton, Nigel J.

Nonlinear functional analysis.

Physical Description:

xii, 255 pages ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2024]

Summary:

"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. 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."--Page 4 of cover.

Contents:

Notations and conventions

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 c₀

Local complementation and the Heinrich-Mankiewicz theorem

The Lipschitz structure of c₀

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)

Appendix A. Vector integration

Appendix B. The Radon-Nikodym property

Appendix C. Gaussian measures

Appendix D. Notes on closest points.

Notes:

Includes bibliographical references (pages 247-251) and index.

Other Format:

Online version: Bowers, Adam (Adam Roman). Nigel Kalton's lectures in nonlinear functional analysis.

ISBN:

9781470473471

147047347X

OCLC:

1456315873