DUALITY, CONVEXITY AND PEAK INTERPOLATION IN THE DRURY-ARVESON SPACE

Abstract. We consider the closed algebra Ad generated by the polynomial multi-pliers on the Drury-Arveson space. We identify A∗d as a direct sum of the preduals of the full multiplier algebra and of a commutative von Neumann algebra, and es-tablish analogues of many classical results concerning the dual space of the ball algebra. These developments are deeply intertwined with the problem of peak in-terpolation for multipliers, and we generalize a theorem of Bishop-Carleson-Rudin to this setting by means of Choquet type integral representations. As a byproduct we shed some light on the nature of the extreme points of the unit ball of A∗d. 1