Functional Analysis

An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras

  • Joseph Muscat

Table of contents

  1. Front Matter
    Pages i-xi
  2. Joseph Muscat
    Pages 1-10
  3. Metric Spaces

    1. Front Matter
      Pages 11-11
    2. Joseph Muscat
      Pages 13-26
    3. Joseph Muscat
      Pages 27-36
    4. Joseph Muscat
      Pages 37-55
    5. Joseph Muscat
      Pages 57-64
    6. Joseph Muscat
      Pages 65-85
  4. Banach and Hilbert Spaces

    1. Front Matter
      Pages 87-87
    2. Joseph Muscat
      Pages 89-114
    3. Joseph Muscat
      Pages 115-138
    4. Joseph Muscat
      Pages 139-169
    5. Joseph Muscat
      Pages 171-219
    6. Joseph Muscat
      Pages 221-256
    7. Joseph Muscat
      Pages 257-274
  5. Banach Algebras

    1. Front Matter
      Pages 275-275
    2. Joseph Muscat
      Pages 277-305
    3. Joseph Muscat
      Pages 307-343
    4. Joseph Muscat
      Pages 345-392
  6. Back Matter
    Pages 393-420

About this book


This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields.

Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.


Banach Algebra Banach Space Functional Analysis Hilbert Space Metric Space

Authors and affiliations

  • Joseph Muscat
    • 1
  1. 1.Mathematics DepartmentUniversity of MaltaMsidaMalta

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-06727-8
  • Online ISBN 978-3-319-06728-5
  • About this book
Industry Sectors