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Functional analysis textbook recommendation needed

  1. Aug 19, 2009 #1
    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.
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  3. Aug 19, 2009 #2


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    Last edited by a moderator: May 4, 2017
  4. Aug 19, 2009 #3
    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 https://www.amazon.com/Elements-The...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.
    Last edited by a moderator: May 4, 2017
  5. Aug 19, 2009 #4

    George Jones

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    I third Kreyszig's functional analysis book. It was the text for a course I took as an undergrad.
  6. Aug 20, 2009 #5
    Last edited by a moderator: May 4, 2017
  7. Aug 20, 2009 #6
    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.
    Last edited: Aug 20, 2009
  8. Sep 13, 2009 #7
    Thank you very much for all the replies.
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