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

### Abstract

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 $A_{0}$, $A_{0}\subseteq A eq A_{0}$. 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 $\mathbb{L}_{2}(\mathbf{R}_{n})$.

### Article Information

 Title Non-negative perturbations of non-negative self-adjoint operators Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 103-109 MathSciNet MR2336722 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

Odessa National I. I. Mechnikov University, Odessa, 65026, Ukraine

### Citation Example

Vadym Adamyan, Non-negative perturbations of non-negative self-adjoint operators, Methods Funct. Anal. Topology 13 (2007), no. 2, 103-109.

### BibTex

@article {MFAT415,
}