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• W2014930482 abstract "The classical Weyl–von Neumann theorem states that for any self-adjoint operator A0 in a separable Hilbert space H there exists a (non-unique) Hilbert–Schmidt operator C=C⁎ such that the perturbed operator A0+C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering the set ExtA of self-adjoint extensions of a given densely defined symmetric operator A in H and some fixed A0=A0⁎∈ExtA. We show that the ac-parts A˜ac and A0ac of A˜=A˜⁎∈ExtA and A0 are unitarily equivalent provided that the resolvent difference KA˜:=(A˜−i)−1−(A0−i)−1 is compact and the Weyl function M(⋅) of the pair {A,A0} admits weak boundary limits M(t):=w-limy→+0M(t+iy) for a.e. t∈R. This result generalizes the classical Kato–Rosenblum theorem. Moreover, it demonstrates that for such pairs {A,A0} the Weyl–von Neumann theorem is in general not true in the class ExtA." @default.
• W2014930482 created "2016-06-24" @default.
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• W2014930482 date "2011-02-01" @default.
• W2014930482 modified "2023-10-02" @default.
• W2014930482 title "On the unitary equivalence of absolutely continuous parts of self-adjoint extensions" @default.
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• W2014930482 doi "https://doi.org/10.1016/j.jfa.2010.10.021" @default.
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