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?

  • 2
    $\begingroup$ 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 . $\endgroup$ – Giuseppe Negro Apr 13 '11 at 18:15

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

  • $\begingroup$ 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. $\endgroup$ – Robert Israel Apr 13 '11 at 23:28
  • $\begingroup$ 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.) $\endgroup$ – wildildildlife Apr 14 '11 at 22:45
  • $\begingroup$ @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. $\endgroup$ – Willie Wong Apr 15 '11 at 2:09

Rudin, "Functional Analysis", chapter 12


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!).

  • 1
    $\begingroup$ I might add that Pedersen and Conway cover normal operators, while Lang only treats self-adjoint operators. $\endgroup$ – wildildildlife Apr 14 '11 at 22:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.