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A Course in Functional Analysis (Graduate Texts in Mathematics) Hardcover – January 25, 1994

ISBN-13: 978-3540960423 ISBN-10: 0387972455 Edition: 2nd

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A Course in Functional Analysis (Graduate Texts in Mathematics) + A Course in Operator Theory (Graduate Studies in Mathematics, Vol. 21) + Fundamentals of the Theory of Operator Algebras (Graduate Studies in Mathematics, V. 15)
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Product Details

  • Series: Graduate Texts in Mathematics (Book 96)
  • Hardcover: 400 pages
  • Publisher: Springer; 2nd edition (January 25, 1994)
  • Language: English
  • ISBN-10: 0387972455
  • ISBN-13: 978-3540960423
  • Product Dimensions: 9.4 x 6.4 x 1.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #298,022 in Books (See Top 100 in Books)

Editorial Reviews

Review

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."

—MATHEMATICAL REVIEWS

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, bookinspections.wordpress.com, October, 2013)

Customer Reviews

4.4 out of 5 stars
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See all 5 customer reviews
This book is a comprehensive introduction to functional analysis.
Josue Rosario
If this and the spectral theorem goal are kept in mind, the omissions and emphasis found in the book will be found to be completely natural.
Kevin R. Vixie
It's a good book for people who have never read this book before, as well as people who are currently studying the course.
Ami

Most Helpful Customer Reviews

27 of 29 people found the following review helpful By Kevin R. Vixie on May 29, 2000
Format: Hardcover
I learned functional analysis by studying this book. I did this under the direction of a master teacher, John Erdman, who taught via a modified Moore Method. I found this very inspirational and challenging. BEFORE I took the course, I did not enjoy browsing the book, BUT I learned that the book, upon combination with the right amount of focus and effort, did a remarkable job of bringing functional analysis alive ... of transmiting the real essence to young, "sprouting" mathematicians. There is also an informality that brings a freshness to the book ... and this in a subject that could easily be studied without encountering this important ingredient in a mathematician's training.
This book has as it's high point and goal the spectral theorem for normal operators. I add this because no one book can be all encompassing. If this and the spectral theorem goal are kept in mind, the omissions and emphasis found in the book will be found to be completely natural.
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 (with an eye to the spectral theorem for normal operators).
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20 of 25 people found the following review helpful By Ami on March 31, 2000
Format: Hardcover
This book is just excellent. The author decides to do something a little unusual, and starts talking about "Hilbert Spaces" before talking about "Banach Spaces". Conway writes down the matereal in a great way. He gives proves to almost every proposition, and gives lots of EXAMPLES and EXCERCISES (which are not given in most of the books about this subject). It's a good book for people who have never read this book before, as well as people who are currently studying the course. Also, conway extends the book's content by writing about advanced subjects (that are not studied in a first course about the subject), like locally convex spaces, weak topologies and even unbounded operators.
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8 of 11 people found the following review helpful By D. Coyle on September 7, 2005
Format: Hardcover Verified Purchase
The only reason for 4 stars instead of 5 is that I am not a great fan of Conway's style, and have wasted too much time on mangled examples in his Complex Analysis.

That said, the layout here is superb, and the choice of topics just what is needed to get one of the ground. Beginners will find it useful to have a copy of Kreyszig at hand.
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1 of 1 people found the following review helpful By Josue Rosario on May 29, 2013
Format: Hardcover
This book is a comprehensive introduction to functional analysis. The style is very formal and rigorous (as it have to be) and you need to have a good background in measure theory and general topology (as it is mentioned in the introduction), chapters 1-4 & 6 of Folland's real analysis book would be more than enough. I think this background is necessary to fully appreciate this excellent book otherwise this book can be difficult and challenging. Do not forget that this book is designed to be used in grad courses. I definitely recommend this book to anyone who really want/need to learn true functional analysis for graduate work. Through its eleven chapters J. Conway masterfully wrote a beautiful exposition of this core subject.

Personally I have never been a follower of Rudin's books, I always have been able to find a substitute for every Rudin's book that match better my taste, and in this case Conway's functional analysis book is undoubtedly my choice. I consider that students interested in operator theory/algebras would appreciate this book even more, you can feel the operator taste throughout the book. Some negative remarks? well I think that the last chapter on Fredholm theory is a bit obscure, it can be largely improved, I would recommend chapter 1 of Gerald Murphy's book C*-algebras and operator theory for a cleaner and more meaningful exposition of Fredholm operators/index.
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9 of 19 people found the following review helpful By Matthew H. Holden on April 27, 2009
Format: Hardcover
This book is appropriate for a graduate course in functional analysis in a mathematics department. It assumes a strong background in undergraduate topology, advanced linear algebra (a linear algebra course that covered direct sums and products, dual spaces, quotient spaces, isomorphisms, and universal mapping properties) and complex analysis, along with a graduate level course in real analysis and measure theory. This book should not be used for a graduate course in Applied Functional Analysis (as it was when I took it). Very few applications are discussed, there is only one diagram in the entire book, proofs skip many intermediate steps, and examples are stated with no explanation. If you do not have the equivalent knowledge of a bachelors in pure mathematics, this book will be almost unreadable. The take home message here is that this book is not for quantitative scientists (who use a lot of functional analysis tools without even knowing it) to study the basic theory behind the tools they use. Its designed for exactly what it says, "a graduate course in mathematics". So if you are a Professor about to teach a course in "Applied Functional Analysis" do not use this book. Use one of the many books called Applied functional analysis.

That being said, I did appreciate the order of coverage. Starting with Hilbert spaces and then moving to Banach spaces, made things more clear for me.
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