Von Neumann's theorem
In mathematics, von Neumann's theorem is a result in the operator theory of linear operators on Hilbert spaces.
Statement of the theorem
[edit]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
[edit]- ^ 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.