Customer Reviews

A Course in Functional Analysis

5 star:		(3)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

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).

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.

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.

I'm learning functional analysis from this book and it's absolutely wonderful. Clear, comprehensive, starts essentially from scratch (it assumes measure theory and linear algebra but nothing else) and deals in detail with what I think is a beautiful subject, the spectral theory of linear operators.

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.