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dc.contributor.advisorMakarov, Konstantin A.eng
dc.contributor.authorSkripka, Anna, 1979-eng
dc.date.issued2007eng
dc.date.submitted2007 Springeng
dc.descriptionThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.eng
dc.descriptionTitle from title screen of research.pdf file (viewed on October 9, 2007)eng
dc.descriptionVita.eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionThesis (Ph. D.) University of Missouri-Columbia 2007.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description.abstractThe dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for the [xi]-index, a spectral parameter independent counterpart of Krein's spectral shift function. The proofs of the main results are based on diverse properties of the operator logarithm and argument averaged with respect to a normal tracial state that are derived in this work. In addition, formula representations for the [xi]-index and the [xi]- function are obtained and the concept of the [xi]-index is related to that of the spectrum distribution function for some random operators.eng
dc.identifier.merlinb60063233eng
dc.identifier.oclc173847195eng
dc.identifier.urihttps://hdl.handle.net/10355/4740
dc.identifier.urihttps://doi.org/10.32469/10355/4740eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.subject.lcshVon Neumann algebraseng
dc.titleTrace formulae in finite von Neumann algebraseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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