Non-trivial singular spectral shift functions exist

Abstract

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 $H.$

10 pages

References in corpus (3)

• Absolutely continuous and singular spectral shift functions
• Infinitesimal spectral flow and scattering matrix
• Singular spectral shift is additive

Cited by in corpus (1)

• Absolutely continuous and singular spectral shift functions