Real spectral shift functions for pairs of contractions and pairs of dissipative operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914424515723264 |
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| author | Malamud, M. M. Neidhardt, H. Peller, V. V. |
| author_facet | Malamud, M. M. Neidhardt, H. Peller, V. V. |
| contents | 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 Schrödinger operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Real spectral shift functions for pairs of contractions and pairs of dissipative operators Malamud, M. M. Neidhardt, H. Peller, V. V. Functional Analysis Classical Analysis and ODEs Complex Variables Spectral Theory 47A55, 47B44, 47A45, 47A60, 47B10 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 Schrödinger operators. |
| title | Real spectral shift functions for pairs of contractions and pairs of dissipative operators |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables Spectral Theory 47A55, 47B44, 47A45, 47A60, 47B10 |
| url | https://arxiv.org/abs/2603.25242 |