For any densely defined operator "A" on Hilbert space one can define its adjoint operator "A". For a symmetric operator "A", the domain of the operator "A" contains the domain of the operator "A", and the restriction of the operator "A" on the domain of "A" coincides with the operator "A", i.e. , in other words "A" is an extension of "A". For a self-adjoint operator "A" the domain of "A" is the same as the domain of "A", and . See also Extensions of symmetric operators and unbounded operator.