A CHARACTERIZATION OF SEMIBOUNDED SELF-ADJOINT OPERATORS

For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension , which coincides with the usual Friedrichs extension when S is semibo unded. In this paper we provide an operator-theoretic interpretation o f this class of symmetric operators. Moreover, we prove that a selfadj oint operator A is semibounded if and only if each one-dimensional res triction of A has a generalized Friedrichs extension.