A Course in Functional Analysis (Hardcover)

by John B. Conway (Author) "A Hilbert space is the abstraction of the finite-dimensional Euclidean spaces of geometry..." (more)
Key Phrases: right modular unit, compact normal operator, closed symmetric extension, Prove Proposition, Hahn-Banach Theorem, Alaoglu's Theorem (more...)

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

Product Description
This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also appreciate the large number of examples and exercises which have been included.

Product Details

• Hardcover: 424 pages
• Publisher: Springer; 2nd edition (January 25, 1994)
• Language: English
• ISBN-10: 0387972455
• ISBN-13: 978-3540960423
• Product Dimensions: 9.4 x 6.3 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #49,634 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

21 of 21 people found the following review helpful:

5.0 out of 5 stars A Course in Functional Analysis ... the title is correct!, May 29, 2000

By	Kevin R. Vixie (Los Alamos, NM) - See all my reviews (REAL NAME)

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).

16 of 19 people found the following review helpful:

5.0 out of 5 stars An Excellent Book !, March 31, 2000

By	Ami (Holon, Israel) - See all my reviews

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.

2 of 2 people found the following review helpful:

3.0 out of 5 stars For Pure Math Courses Only, April 27, 2009

By	Matthew H. Holden - See all my reviews (REAL NAME)

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.