An Introductory Course in Functional Analysis

  • Adam Bowers
  • Nigel J. Kalton
Book

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 1-9
  3. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 11-29
  4. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 31-60
  5. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 61-82
  6. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 83-127
  7. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 129-150
  8. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 151-180
  9. Adam Bowers, Nigel J. Kalton (deceased)
    Pages 181-206
  10. Back Matter
    Pages 207-232

About this book

Introduction

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 HahnBanach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the MilmanPettis 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.

Keywords

Baire category theorem Banach space Hahn-Banach extension theorems Wiener inversion theorem functional analysis normed spaces

Authors and affiliations

  • Adam Bowers
    • 1
  • Nigel J. Kalton
    • 2
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.University of Missouri, Columbia Dept. MathematicsColumbiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-1945-1
  • Copyright Information Springer Science+Business Media, LLC 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-1944-4
  • Online ISBN 978-1-4939-1945-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book