Abstract :

This is a continuation of last week's talk on the Kadison Singer problem and Anderson's Paving conjecture. 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 talk, we will see how Anderson's Paving conjecture implies the Kadison-Singer conjecture.