Non-negative perturbations of non-negative self-adjoint operators

Details Non-negative perturbations of non-negative self-adjoint operators Non-negative perturbations of non-negative self-adjoint operators

2007-01-02

arxiv.org/abs/math-ph/0701004v1

Physics

Mathematical Physics

08 pages

Scientific paper

Let $A$ be a non-negative self-adjoint operator in a Hilbert space $\mathcal{H}$ and $A_{0}$ be some densely defined closed restriction of $A_{0}$, $A_{0}\subseteq A \neq A_{0}$. It is of interest to know whether $A$ is the unique non-negative self-adjoint extensions of $A_{0}$ in $\mathcal{H}$. We give a natural criterion that this is the case and if it fails, we describe all non-negative extensions of $A_{0}$. The obtained results are applied to investigation of non-negative singular point perturbations of the Laplace and poly-harmonic operators in $\mathbb{L}_{2}(\mathbf{R}_{n})$.

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