Non-negative Perturbations of Non-negative Self-adjoint Operators
نویسنده
چکیده
Let A be a non-negative self-adjoint operator in a Hilbert space H and A0 be some densely defined closed restriction of A0, A0 ⊆ A 6= A0. It is of interest to know whether A is the unique non-negative self-adjoint extensions of A0 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 L2(Rn).
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