Let $A_\N$ be the symmetric operator given by the restriction of $A$ to $\N$, where $A$ is a self-adjoint operator on the Hilbert space $\H$ and $\N$ is a linear dense set which is closed with respect to the graph norm on $D(A)$, the operator domain of $A$. We show that any self-adjoint extension $A_\Theta$ of $A_\N$ such that $D(A_\Theta)\cap D(A)=\N$ can be additively decomposed by the sum $A_\Theta=\A+T_\Theta$, where both the operators $\A$ and $T_\Theta$ take values in the strong dual of...

Source: http://arxiv.org/abs/math/0104226v2