non-negative self-adjoint operators, write if, and only if, Theorem. There are unique self-adjoint extensions Tmin and Tmax of any non-negative symmetric operator T such that and every non-negative self-adjoint extension S of T is between Tmin and Tmax, i.e. See also Energetic extension Extensions of symmetric operators Notes References N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Pitman, 1981. Operator theory Linear operators