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I am looking for a book that develops the theory of Hilbert spaces, including the spectral theorems and unitary representations, but includes non-separable Hilbert spaces in the main exposition. Any special results for separable Hilbert spaces are carefully marked as such, so as not to confuse the main exposition, which includes non-separable Hilbert spaces.

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Halmos's Introduction to Hilbert space and the theory of spectral multiplicity is what you are looking for. Since it's published by Dover, the price is very reasonable.

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  • $\begingroup$ Thanks. I've ordered the book. The length of only 120 pages had suggested to me that this would not be a rigorous exposition. I shouldn't judge a book by its cover! Can't go wrong, though, with the $15 price. $\endgroup$
    – Norman Goldstein
    Commented Apr 21 at 16:49

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