As far as the simplest spectral theorem for bounded selfadjoint operators, more precise statement (than at spectral theorem) can be found at spectral theorem for bounded selfadjoint operators (zoranskoda).

As far as normal operators, I hope I can add something later, but just to mention: of course the C-star algebra definition assumes boundedness so it has a false appearance as a more general definition; unbounded normal operators should be maybe defined separately, because of the domain of the definition both of the operator and of its adjoint which are not the entire space. I may get back to this later if somebody else will not be quicker. Thanks for starting the stub!

]]>created a stub for normal operator and noticed/remembered that Tim van Beek had once created the beginning of an entry spectral theorem that he ended with an empty section on the version for normal operators. If we are lucky he will come back some day and complete this, but it looks like he wonâ€™t. Maybe somebody else feels inspired to work on this entry.

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