Von Neumann's theorem

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

be Hilbert spaces, and let

: dom ⁡ (

{\displaystyle T:\operatorname {dom} (T)\subseteq G\to H}

be an unbounded operator from

is a closed operator and that

is densely defined, that is,

denote the adjoint of

is also densely defined, and it is self-adjoint.

and the operators on the right- and left-hand sides have the same dense domain in