(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Arslan, İlker.; Tanbay, Betül.
Let 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.