Resources for Math 502

There is no textbook for this course. If you would like to consult a book, I have some suggestions.

The book by Kreyszig is the most popular introductory functional analysis textbook. It's the one I used last time I taught the course, but I don't like it.

I have also used the book by MacCluer once. Its virtues are that it is a fairly compact book that covers the main material and is reasonably priced. Its C-star-algebra approach to spectral theory is appealing, but it is beyond the scope of our course.

I learned a lot from the book by Riesz and Nagy when I was a graduate student. This is one of the first textbooks on functional analysis, published originally in French in 1953. Of course it's dated, but I think it is still a very useful book. It's now available as a Dover paperback, so you can get your own copy at a reasonable price.

I took a course in Functional Analysis from the first edition of Taylor's book around 1970. There is a lot in this book. It presents the theory in great generality, perhaps too great.

Of course, there are many other books on functional analysis that you might consult, and there is also a great deal of material on the web.

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