© 2014

An Introductory Course in Functional Analysis


  • 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


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


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.


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

Authors and affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.University of Missouri, Columbia Dept. MathematicsColumbiaUSA

About the authors

Nigel Kalton (1946–2010) was Curators' Professor of Mathematics at the University of Missouri. Adam Bowers is a mathematics lecturer at the University of California, San Diego.

Bibliographic information

  • Book Title An Introductory Course in Functional Analysis
  • Authors Adam Bowers
    Nigel J. Kalton
  • Series Title Universitext
  • Series Abbreviated Title Universitext
  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-1-4939-1944-4
  • eBook ISBN 978-1-4939-1945-1
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages XVI, 232
  • Number of Illustrations 2 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


“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)