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