In the fifties, Kadison and Singer conjectured the following : Any pure state on DD extends uniquely to a state on B(l2)B(l2) where B(l2)B(l2) is the set of all bounded operators on the Hilbert space l2l2 and DD is the set of all diagonal operators in B(l2)B(l2). In the first talk, we went over the basic material related to this topic and in particular explained the Anderson Paving conjecture. In this talk, we will see how Anderson's Paving conjecture implies the Kadison-Singer conjecture.
