© 2007

A Course in Functional Analysis


Part of the Graduate Texts in Mathematics book series (GTM, volume 96)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. John B. Conway
    Pages 1-25
  3. John B. Conway
    Pages 26-62
  4. John B. Conway
    Pages 63-98
  5. John B. Conway
    Pages 99-123
  6. John B. Conway
    Pages 124-165
  7. John B. Conway
    Pages 166-186
  8. John B. Conway
    Pages 232-254
  9. John B. Conway
    Pages 255-302
  10. John B. Conway
    Pages 303-346
  11. John B. Conway
    Pages 347-368
  12. Back Matter
    Pages 369-403

About this book


Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.


Analysis Banach Space C*-algebra Hilbert space calculus differential equation functional analysis measure

Authors and affiliations

  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

About the authors


Bibliographic information

  • Book Title A Course in Functional Analysis
  • Authors John B Conway
  • Series Title Graduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-97245-9
  • Softcover ISBN 978-1-4419-3092-7
  • eBook ISBN 978-1-4757-4383-8
  • Series ISSN 0072-5285
  • Edition Number 2
  • Number of Pages XVI, 400
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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Second Edition

J.B. Conway

A Course in Functional Analysis

"This book is an excellent text for a first graduate course in functional analysis . . . Many interesting and important applications are included . . . This book is a fine piece of work. It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author."


From the reviews of the second edition:

“This book should be in the library of anyone teaching functional analysis or who wants a working mathematician’s masterfully developed course on functional analysis … . This book is a comprehensive introduction to functional analysis. … I definitely recommend this book to anyone who really want/need to learn true functional analysis for graduate work.” (Philosophy, Religion and Science Book Reviews,, October, 2013)