Abstract :

In the fifties, Kadison and Singer conjectured the following : Any pure state on $D$ extends uniquely to a state on $B(l^2)$ where $B(l^2)$ is the set of all bounded operators on the Hilbert space $l^2$ and $D$ is the set of all diagonal operators in $B(l^2)$. In this (first) talk, I will go over the basic material related to this topic (whatever is needed) and in particular, will explain the Anderson Paving conjecture. (In next week's talk, we will see how Anderson's Paving conjecture implies the Kadison-Singer conjecture.)