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arXiv · 2603.25242

Real spectral shift functions for pairs of contractions and pairs of dissipative operators

M. M. Malamud·H. Neidhardt·V. V. Peller
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Abstract

Recently the authors solved a long-standing problem and showed that for an arbitrary pair of contractions on Hilbert space with trace class difference has an integrable spectral shift function on the unit circle ${\Bbb T}$ and an analogue of the Lifshits--Krein trace formula holds. It is also known that it may happen that there is no real-values integrable spectral shift function. In this paper we find conditions under which a pair of contractions with trace class difference has {\it a real-valued integrable} spectral shift function. We also consider a similar problem for pairs of dissipative operators. Finally, we find an application of the results in question to dissipative Schr\"odinger operators.

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M. M. Malamud, H. Neidhardt, V. V. Peller. 2026-03-26. Real spectral shift functions for pairs of contractions and pairs of dissipative operators. https://arxiv.org/abs/2603.25242

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