Normal operatörler için spektral katlılığa ölçüm çözünümü yaklaşımı

In this thesis we studied the notion of direct integral Hilbert spaces, first introducedby J. von Neumann, and the closely related notion of decomposableoperators, as defined in Kadison and Ringrose [1997] and Abrahamse and Kriete[1973]. Examples which show that some of the most familiar spaces in analysisare direct integral Hilbert spaces are presented in detail. Then we give a carefultreatment of the notion of disintegration of a probability measure on a locallycompact separable metric space, and using the machinery we obtain, a proof ofthe Spectral Multiplicity Theorem for Normal Operators employing the notionof disintegration of measures is given, based on Abrahamse and Kriete [1973],Arveson [1976], Arveson [2002]. In Chapter 5 the notion of essential preimage ispresented in the sense of the article Abrahamse and Kriete [1973], and its relationwith the spectral multiplicity function is discussed.