Lebesgue-radon-nikodym decompositions for operator valued completely positice maps

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buir.advisorGheondea, Aurelian
dc.contributor.authorDanış, Bekir
dc.date.accessioned2016-01-08T18:28:02Z
dc.date.available2016-01-08T18:28:02Z
dc.date.issued2014
dc.descriptionAnkara : The Department of Mathematics and the Granduate School of Engineering and Science of Bilkent University, 2014.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2014.en_US
dc.descriptionIncludes bibliographical references leaves leaf 28.en_US
dc.description.abstractWe discuss the notion of Radon-Nikodym derivatives for operator valued completely positive maps on C*-algebras, first introduced by Arveson [1969], and the notion of absolute continuity for completely positive maps, previously introduced by Parthasarathy [1996]. We begin with the definition and basic properties of positive and complete positive maps and we study the Stinespring dilation theorem which plays an essential role in the theory of Radon-Nikodym derivatives for completely positive maps, based on Poulsen [2002]. Then, the Radon-Nikodym derivative definition and basic properties belonging to Arveson is recorded and finally, we study the Lebesgue type decompositions defined by Parthasarathy in the light of the article Gheondea and Kavruk [2009].en_US
dc.description.provenanceMade available in DSpace on 2016-01-08T18:28:02Z (GMT). No. of bitstreams: 1 0006684.pdf: 271930 bytes, checksum: 8675f0ce6272884c7e1c7d7aadc56a87 (MD5)en
dc.description.statementofresponsibilityDanış, Bekiren_US
dc.format.extentvi, 33 leavesen_US
dc.identifier.urihttp://hdl.handle.net/11693/15980
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectRadon-Nikodym derivativesen_US
dc.subjectcompletely positive mapsen_US
dc.subjectC*-algebrasen_US
dc.subjectabsolute continuityen_US
dc.subjectstinespring representationen_US
dc.subjectnon-commutative lebesgue decompositionsen_US
dc.subject.lccQA312.5 .D35 2014en_US
dc.subject.lcshLebesgue-Radon-Nikodym theorem.en_US
dc.subject.lcshLebesgue integral.en_US
dc.subject.lcshMeasure theory.en_US
dc.titleLebesgue-radon-nikodym decompositions for operator valued completely positice mapsen_US
dc.typeThesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorBilkent University
thesis.degree.levelMaster's
thesis.degree.nameMS (Master of Science)

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