Real-valued spectral shift functions for contractions and dissipative operators
In recent joint papers the authors of this note solved a famous problem remained open for many years and proved that for arbitrary contractions with trace class difference there exists an integrable spectral shift function, for which an analogue of the Lifshits--Krein trace formula holds. Similar re...
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| creator | Malamud, Mark M Neidhardt, H Peller, Vladimir V |
| description | In recent joint papers the authors of this note solved a famous problem
remained open for many years and proved that for arbitrary contractions with
trace class difference there exists an integrable spectral shift function, for
which an analogue of the Lifshits--Krein trace formula holds. Similar results
were also obtained for pairs of dissipative operators. Note that in contrast
with the case of self-adjoint and unitary operators it may happen that there is
no {\it real-valued} integrable spectral shift function. In this note we
announce results that give sufficient conditions for the existence of an
integrable real-valued spectral shift function in the case of pairs of
contractions. We also consider the case of pairs of dissipative operators. |
| doi_str_mv | 10.48550/arxiv.2410.22529 |
| format | Article |
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remained open for many years and proved that for arbitrary contractions with
trace class difference there exists an integrable spectral shift function, for
which an analogue of the Lifshits--Krein trace formula holds. Similar results
were also obtained for pairs of dissipative operators. Note that in contrast
with the case of self-adjoint and unitary operators it may happen that there is
no {\it real-valued} integrable spectral shift function. In this note we
announce results that give sufficient conditions for the existence of an
integrable real-valued spectral shift function in the case of pairs of
contractions. We also consider the case of pairs of dissipative operators.</description><identifier>DOI: 10.48550/arxiv.2410.22529</identifier><language>eng</language><subject>Mathematics - Classical Analysis and ODEs ; Mathematics - Complex Variables ; Mathematics - Functional Analysis ; Mathematics - Spectral Theory</subject><creationdate>2024-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2410.22529$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2410.22529$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Malamud, Mark M</creatorcontrib><creatorcontrib>Neidhardt, H</creatorcontrib><creatorcontrib>Peller, Vladimir V</creatorcontrib><title>Real-valued spectral shift functions for contractions and dissipative operators</title><description>In recent joint papers the authors of this note solved a famous problem
remained open for many years and proved that for arbitrary contractions with
trace class difference there exists an integrable spectral shift function, for
which an analogue of the Lifshits--Krein trace formula holds. Similar results
were also obtained for pairs of dissipative operators. Note that in contrast
with the case of self-adjoint and unitary operators it may happen that there is
no {\it real-valued} integrable spectral shift function. In this note we
announce results that give sufficient conditions for the existence of an
integrable real-valued spectral shift function in the case of pairs of
contractions. We also consider the case of pairs of dissipative operators.</description><subject>Mathematics - Classical Analysis and ODEs</subject><subject>Mathematics - Complex Variables</subject><subject>Mathematics - Functional Analysis</subject><subject>Mathematics - Spectral Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjsEKwjAQRHPxIOoHeHJ_oLXGFvQsijdBvJelTXAhJmE3Lfr31tK7p4E3A_OUWu-KvDxUVbFFflOf63IAWlf6OFe3u0GX9eg604JE0yRGB_Ikm8B2vkkUvIANDE3wQzcB9C20JEIRE_UGQjSMKbAs1cyiE7OacqE2l_PjdM3G6zoyvZA_9U-hHhX2_xdfQH89cA</recordid><startdate>20241029</startdate><enddate>20241029</enddate><creator>Malamud, Mark M</creator><creator>Neidhardt, H</creator><creator>Peller, Vladimir V</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20241029</creationdate><title>Real-valued spectral shift functions for contractions and dissipative operators</title><author>Malamud, Mark M ; Neidhardt, H ; Peller, Vladimir V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2410_225293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Classical Analysis and ODEs</topic><topic>Mathematics - Complex Variables</topic><topic>Mathematics - Functional Analysis</topic><topic>Mathematics - Spectral Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Malamud, Mark M</creatorcontrib><creatorcontrib>Neidhardt, H</creatorcontrib><creatorcontrib>Peller, Vladimir V</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Malamud, Mark M</au><au>Neidhardt, H</au><au>Peller, Vladimir V</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Real-valued spectral shift functions for contractions and dissipative operators</atitle><date>2024-10-29</date><risdate>2024</risdate><abstract>In recent joint papers the authors of this note solved a famous problem
remained open for many years and proved that for arbitrary contractions with
trace class difference there exists an integrable spectral shift function, for
which an analogue of the Lifshits--Krein trace formula holds. Similar results
were also obtained for pairs of dissipative operators. Note that in contrast
with the case of self-adjoint and unitary operators it may happen that there is
no {\it real-valued} integrable spectral shift function. In this note we
announce results that give sufficient conditions for the existence of an
integrable real-valued spectral shift function in the case of pairs of
contractions. We also consider the case of pairs of dissipative operators.</abstract><doi>10.48550/arxiv.2410.22529</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables Mathematics - Functional Analysis Mathematics - Spectral Theory |
| title | Real-valued spectral shift functions for contractions and dissipative operators |
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