Analysis Seminar

Ken Davidson, Department of Pure Mathematics, University of Waterloo

“Choquet order and hyperrigidity for function systems”

Choquet theory studies representing measures for states on the space of affine functions of a compact convex set. The Choquet order on measures is used to establish that there is always a representing measure supported on the set of extreme points (in a technical sense). We introduce a new operator-theoretic order on measures, and prove that it is equivalent to the Choquet order. This leads to some improvements in the classical theory, but more importantly it leads to some new operator-theoretic consequences. In particular, we establish Arveson’s hyperrigidity conjecture for function systems, which in turn yields a significant strengthening of the classical approximation theorems of Korovkin and S ̆a ̆skin.

This is joint work with Matthew Kennedy.

MC 5417