Spectral Theorem for Unitary Operator

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It is well known that the following - in many literature - called the Spectral Theorem for Unitary Operator.

I would like to know where i can find further information about it and its proof.

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1 Answer

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There is nothing special about being unitary here. The key property is that unitaries operators are normal. So you should search for the Spectral Theorem for normal operators.

One source I know is Section IX.2 in Conway's A Course in Functional Analysis.

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