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A Course in Functional Analysis

  • Textbook
  • © 2007
  • Latest edition


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

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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.

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Table of contents (11 chapters)


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)

Authors and Affiliations

  • Department of Mathematics, University of Tennessee, Knoxville, USA

    John B. Conway

About the author


Bibliographic Information

  • Book Title: A Course in Functional Analysis

  • Authors: John B. Conway

  • Series Title: Graduate Texts in Mathematics

  • DOI:

  • Publisher: Springer New York, NY

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

  • Copyright Information: Springer-Verlag New York 2007

  • Hardcover ISBN: 978-0-387-97245-9Published: 07 September 1990

  • Softcover ISBN: 978-1-4419-3092-7Published: 01 December 2010

  • eBook ISBN: 978-1-4757-4383-8Published: 09 March 2019

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XVI, 400

  • Topics: Analysis

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