Overview
- Presents the basics of functional analysis according to Nigel Kalton, a leader in the field
- Enables the reader to appreciate and apply the theory by explaining both the why and how of the subject's development
- Gives novel proofs of major theorems, such as the Hahn–Banach theorem, Schauder's theorem, and the Milman–Pettis theorem
- Contains over 150 exercises to develop and enrich the reader's understanding of the subject
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
Keywords
About this book
Based on a graduate course by the celebrated analyst Nigel Kalton, this well-balanced introduction to functional analysis makes clear not only how, but why, the field developed. All major topics belonging to a first course in functional analysis are covered. However, unlike traditional introductions to the subject, Banach spaces are emphasized over Hilbert spaces, and many details are presented in a novel manner, such as the proof of the Hahn–Banach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the Milman–Pettis theorem.
With the inclusion of many illustrative examples and exercises, An Introductory Course in Functional Analysis equips the reader to apply the theory and to master its subtleties. It is therefore well-suited as a textbook for a one- or two-semester introductory course in functional analysis or as a companion for independent study.
Reviews
“The text is very well written. Great care is taken to discuss interrelations of results. … Each chapter ends with well selected exercises, typically around 20 exercises per chapter. … I believe that this book is also suitable for self-study by an interested student. It can also serve as an excellent, concise reference for researchers in any area of mathematics seeking to recall/clarify fundamental concepts/results from functional analysis, in their proper context.” (Beata Randrianantoanina, zbMATH 1328.46001, 2016)
“The book is a nicely and economically designed introduction to functional analysis, with emphasis on Banach spaces, that is well-suited for a one- or two-semester course.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 181, 2016)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: An Introductory Course in Functional Analysis
Authors: Adam Bowers, Nigel J. Kalton
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4939-1945-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2014
Softcover ISBN: 978-1-4939-1944-4Published: 12 December 2014
eBook ISBN: 978-1-4939-1945-1Published: 11 December 2014
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XVI, 232
Number of Illustrations: 2 b/w illustrations
Topics: Functional Analysis