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Functional Analysis

An Introductory Course

  • Textbook
  • © 2018

Overview

Authors:
  1. Sergei Ovchinnikov

    1. Department of Mathematics, San Francisco State University, San Francisco, USA

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  • Provides an elementary treatment of the subject that establishes the foundation for further study
  • Enriches understanding of the theory with numerous examples and counterexamples
  • Includes many exercises for readers to practice techniques
  • Dissects proofs of difficult results into small steps to improve understanding
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    • Sergei Ovchinnikov
    Pages 1-17

  3. Metric Spaces

    • Sergei Ovchinnikov
    Pages 19-46

  4. Special Spaces

    • Sergei Ovchinnikov
    Pages 47-73

  5. Normed Spaces

    • Sergei Ovchinnikov
    Pages 75-99

  6. Linear Functionals

    • Sergei Ovchinnikov
    Pages 101-130

  7. Fundamental Theorems

    • Sergei Ovchinnikov
    Pages 131-148

  8. Hilbert Spaces

    • Sergei Ovchinnikov
    Pages 149-191

  9. Back Matter

    Pages 193-205
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Keywords

About this book

This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Boundedness Theorem, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text.



Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.


Reviews

“This textbook is well organized and the proofs are carefully written. … Each chapter is concluded with an interesting note and several exercises, helping the reader to better understand the topics of the chapter. … it will be useful for upper-undergraduate and beginning graduate students.” (Mohammad Sal Moslehian, zbMATH 1398.46001, 2018)

Authors and Affiliations

  • Department of Mathematics, San Francisco State University, San Francisco, USA

    Sergei Ovchinnikov

About the author

Sergei Ovchinnikov is Professor Emeritus of Mathematics at San Francisco State University. His other Universitext books are Measure, Integral, Derivative: a Course on Lebesgue's Theory (2013) and Graphs and Cubes (2011). 

Bibliographic Information

  • Book Title: Functional Analysis

  • Book Subtitle: An Introductory Course

  • Authors: Sergei Ovchinnikov

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-319-91512-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-91511-1Published: 29 June 2018

  • eBook ISBN: 978-3-319-91512-8Published: 09 June 2018

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 205

  • Number of Illustrations: 13 b/w illustrations

  • Topics: Functional Analysis

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