Danış, Bekir2016-01-082016-01-082014http://hdl.handle.net/11693/15980Ankara : The Department of Mathematics and the Granduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves leaf 28.We 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].vi, 33 leavesEnglishinfo:eu-repo/semantics/openAccessRadon-Nikodym derivativescompletely positive mapsC*-algebrasabsolute continuitystinespring representationnon-commutative lebesgue decompositionsQA312.5 .D35 2014Lebesgue-Radon-Nikodym theorem.Lebesgue integral.Measure theory.Thesis