NON-NEGATIVE PERTURBATIONS OF NON-NEGATIVE SELF-ADJOINT OPERATORS

Let A be a non-negative self-adjoint operator in a Hilbert space H and A(0) be some densely defined closed restriction of A(0), A(0) subset of A 6 not equal A(0). It is of interest to know whether A is the unique non-negative self-adjoint extensions of A(0) in H. We give a natural criterion that this is the case and if it fails, we describe all non-negative extensions of A0. The obtained results are applied to investigation of non-negative singular point perturbations of the Laplace and poly-harmonic operators in L-2(R-n).