# references for the spectral theorem

Recently, I am thinking about the question in spectral theory. And I finally found that I need help with the properties of unitary operator. Its a consequence of the spectral theorem for the normal operator, as the wiki says. The spectral theorem in the book I have ever read is only for self-adjoint operator and without many details.

Could anybody here recommend me some references for this theorem?

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This is not exactly what you need, but I think it's worth mentioning anyway: Halmos' article *What does the spectral theorem say?", here: jstor.org/pss/2313117 . – Giuseppe Negro Apr 13 '11 at 18:15

## 3 Answers

Reed and Simon, Methods of Modern Mathematical Physics, Volume 1, Chapter 8.

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I would have mentioned Reed and Simon, but their treatment of the spectral theorem is for self-adjoint operators, the version for normal operators (which is what Jack was asking about) being relegated to the exercises. – Robert Israel Apr 13 '11 at 23:28
Yes, that's what I was thinking too. (So it is perhaps a bit strange that the answer which does not exactly answer the question is accepted.) – wildildildlife Apr 14 '11 at 22:45
@Robert: you are probably right. I don't have my copy handy so was giving the reference based on memory + TOC, the former of which may likely have confused exercise for statement. @Wild: even stranger happens on this site at times. – Willie Wong Apr 15 '11 at 2:09

Rudin, "Functional Analysis", chapter 12

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Conway, Functional Analysis, Chapter IX.

Pedersen, Analysis NOW, Section 4.4 & 4.5.

Lang, Real and Functional Analysis, Chapters XVIII, XIX, XX (yes this is a long book!).

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I might add that Pedersen and Conway cover normal operators, while Lang only treats self-adjoint operators. – wildildildlife Apr 14 '11 at 22:52