High Quality Content by WIKIPEDIA articles! In mathematics, von Neumann's theorem is a result in the operator theory of linear operators on Hilbert spaces.Let G and H be Hilbert spaces, and let T : dom(T) ? G ? H be a densely-defined operator from G into H. Let T? : dom(T?) ? H ? G denote the Hilbert adjoint of T. Suppose that T is a closed operator and that T is densely defined, i.e. dom(T) is dense in G. Then T?T is also densely defined and self-adjoint. That is,and the operators on the right- and let-hand sides have the same dense domain in G.

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