Non-trivial singular spectral shift functions exist

Details Non-trivial singular spectral shift functions exist Non-trivial singular spectral shift functions exist

2010-08-25

arxiv.org/abs/1008.4231v1

Mathematics

Spectral Theory

10 pages

Scientific paper

In this paper I prove existence of an irreducible pair of operators $H$ and
$H+V,$ where $H$ is a self-adjoint operator and $V$ is a self-adjoint
trace-class operator, such that the singular spectral shift function of the
pair is non-zero on the absolutely continuous spectrum of the operator $H.$

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