  The classical Weyl-von Neumann theorem states that for any self-adjoint
operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a
(non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed
operator $A+C$ has purely point spectrum. We are interesting whether this
result remains valid for non-additive perturbations by considering self-adjoint
extensions of a given densely defined symmetric operator $A$ in $\mathfrak H$
and fixing an extension $A_0 = A_0^*$. We show that for a wide class of
symmetric operators the absolutely continuous parts of extensions $\widetilde A
= {\widetilde A}^*$ and $A_0$ are unitarily equivalent provided that their
resolvent difference is a compact operator. Namely, we show that this is true
whenever the Weyl function $M(\cdot)$ of a pair $\{A,A_0\}$ admits bounded
limits $M(t) := \wlim_{y\to+0}M(t+iy)$ for a.e. $t \in \mathbb{R}$. This result
is applied to direct sums of symmetric operators and Sturm-Liouville operators
with operator potentials.
