The classical Weyl-von Neumann theorem states that for any self-adjoint
operator A in a separable Hilbert space 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 H
and fixing an extension A0=A0∗. We show that for a wide class of
symmetric operators the absolutely continuous parts of extensions A=A∗ and A0 are unitarily equivalent provided that their
resolvent difference is a compact operator. Namely, we show that this is true
whenever the Weyl function M(⋅) of a pair {A,A0} admits bounded
limits M(t) := \wlim_{y\to+0}M(t+iy) for a.e. t∈R. This result
is applied to direct sums of symmetric operators and Sturm-Liouville operators
with operator potentials