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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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

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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

I'll take a look-see. Thanks for the tip!

-Dan