Functional analysis textbook recommendation needed

[wasia]

Could any of you recommend a functional analysis textbook?

I have looked at "Methods of modern mathematical physics" by Reed&Simon, but they assume a pure-maths BSc background, thus this book is not ideal for me. About my background: I have an Applied Physics BSc and starting a Theoretical Physics master program with emphasis on strings and QFT.

Mostly I am interested in Hilbert spaces, as well as other things that have (possibly indirect) connections to quantum field theory/quantum mechanics, such as Banach spaces, topological spaces or operators.

[Landau]

If Reed+Simon is too mathematical for you, you should definitely check out Kreyszig' Introductory Functional Analysis with Applications (http://www.amazon.com/Introductory-Functional-Analysis-Applications-Kreyszig/dp/0471504599). If that's too easy, Linear Functional Analysis (http://www.amazon.com/Functional-Analysis-Springer-Undergraduate-Mathematics/dp/1848000049/ref=sr_1_1?ie=UTF8&s=books&qid=1250675792&sr=1-1) by Rynne+Youngson is in between them.

PS: there is a subforum called Science Book Discussion (http://www.physicsforums.com/forumdisplay.php?f=21)

[n!kofeyn]

I second Kreyszig's functional analysis book. I actually plan to go through it myself soon. Another introductory book that I found when searching for this topic is Elements of the Theory of Functions and Functional Analysis (http://www.amazon.com/Elements-Theory-Functions-Functional-Analysis/dp/0486406830/ref=sr_1_1?ie=UTF8&s=books&qid=1250710529&sr=8-1) by Kolmogorov and Fomin. It is much cheaper than Kreysig's book, although from browsing through Kreyszig's book, he was very clear, gave good proofs, and had lots of examples.

[George Jones]

I third Kreyszig's functional analysis book. It was the text for a course I took as an undergrad.

[qspeechc]

http://www.amazon.com/Introductory-Functional-Analysis-Applications-Mathematics/dp/0387983074/ref=sr_1_1?ie=UTF8&s=books&qid=1250782854&sr=8-1

[Pinu7]

Kolmogorov's Elements of the Theory of Functions and Functional Analysis, is one of the best mathematical texts I have. If you don't have it, I'd recommend it.(It's also cheap! $11)

It is a rigorous but enjoyable read. I am currently reading it out of pleasure.

It takes you from set theory to Abstract Hilbert Spaces.

[wasia]

Thank you very much for all the replies.