In mathematics, von Neumann's theorem is a result in the operator theory of linear operators on Hilbert spaces.

Statement of the theorem

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Let   and   be Hilbert spaces, and let   be an unbounded operator from   into   Suppose that   is a closed operator and that   is densely defined, that is,   is dense in   Let   denote the adjoint of   Then   is also densely defined, and it is self-adjoint. That is,   and the operators on the right- and left-hand sides have the same dense domain in  [1]

References

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  1. ^ Acuña, Pablo (2021). "von Neumann's Theorem Revisited". Foundations of Physics. 51 (3): 73. doi:10.1007/s10701-021-00474-5. ISSN 0015-9018. S2CID 237887405.