Abstract: The deepest results of Choquet theory deal with compact sets which are generally not metrizable. We introduce a new approach to Choquet theory that allows us to generalize certain important classical results from the metrizable case to compact Hausdorff spaces. One of these results is Saskin’s Theorem on approximation by a sequence of positive linear maps. Then we discuss a non-commutative version conjectured by Arveson. We show how our approach sheds light on his conjecture.

(This is joint work with Matthew Kennedy.)

Zoom Meeting ID: 953 4937 9380