Graduate Program in Mathematics.Tanbay, Betül.Arslan, İlker.2023-03-162023-03-162010.MATH 2010 A77https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15250Let H be a separable Hilbert space and B(H) be the space of all bounded linear operators on H. A state of a C -algebra is a positive linear functional of norm 1. An extreme point of the set of states is called a pure state. The Kadison-Singer problem asks whether every pure state of the space of the diagonal operators on H extends to a unique pure state or not. In this thesis, after understanding the Kadison-Singer problem, the article "A note on the Kadison-Singer problem" is discussed. This article concludes an interesting result that these extensions either lie in a nite dimensional subspace or contains a homeomorphic copy of N.30cm.Mathematics.vii, 49 leaves;