Raphael Clouatre, Department of Pure Mathematics, University of Waterloo
“Henkin measures for the multiplier algebra of the Drury-Arveson space”
A measure on the sphere is said to be Henkin for the ball algebra if it has a certain weak-* continuity property. Such measures are completely characterized by a classical theorem due to Henkin and Cole-Range, and they can be used in the context of operator theory to show that a ”constrained” absolutely continuous contraction must be pure. Motivated by the corresponding question for commuting row contractions, we investigate Henkin measures for the multiplier algebra Ad of the Drury-Arveson space and we give a description of the dual of that algebra. Our results turn out to mirror the case of the ball algebra, although the techniques needed are vastly different as Ad is not a uniform algebra. We also obtain an analogue of the classical Rudin-Carleson theorem on peak interpolation. (Joint work with Ken Davidson.)