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Math Help - Infinite dimensional Hilbert spaces

  1. #1
    Forum Admin topsquark's Avatar
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    Infinite dimensional Hilbert spaces

    Anyone have any thoughts about where (book, website, etc.) I could find theorems on infinite dimensional Hilbert spaces? I'm a Physicist and all of my personal references (i.e. textbooks) do proofs of theorems in a finite number of dimensions, then blithely tells me that the result also holds for infinite dimensions, but won't take up the case and show me how to do it. For example, the book will prove theorems using a finite discrete basis, then say that the theorems also happen to be true using an infinite basis, such as an infinite set of orthogonal functions. It's not that I don't believe them, it's just I'd like to see how to do it.

    Thanks!
    -Dan
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by topsquark
    Anyone have any thoughts about where (book, website, etc.) I could find theorems on infinite dimensional Hilbert spaces? I'm a Physicist and all of my personal references (i.e. textbooks) do proofs of theorems in a finite number of dimensions, then blithely tells me that the result also holds for infinite dimensions, but won't take up the case and show me how to do it. For example, the book will prove theorems using a finite discrete basis, then say that the theorems also happen to be true using an infinite basis, such as an infinite set of orthogonal functions. It's not that I don't believe them, it's just I'd like to see how to do it.

    Thanks!
    -Dan
    Almost any text with a title contain the term "Functional Analysis" I would
    have thought. You cold start on line with William Chen's lecture notes on
    Functional Analysis

    RonL
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  3. #3
    Forum Admin topsquark's Avatar
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    I'll take a look-see. Thanks for the tip!

    -Dan
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