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


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 $\mathbb{L}_{2}(\mathbf{R}_{n})$.

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TitleNon-negative perturbations of non-negative self-adjoint operators
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 103-109
MathSciNet   MR2336722
CopyrightThe Author(s) 2007 (CC BY-SA)

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

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


@article {MFAT415,
    AUTHOR = {Adamyan, Vadym},
     TITLE = {Non-negative perturbations of non-negative self-adjoint operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {103-109},
      ISSN = {1029-3531},
  MRNUMBER = {MR2336722},
       URL = {},

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