  We consider the closed algebra $\mathcal{A}_d$ generated by the polynomial
multipliers on the Drury-Arveson space. We identify $\mathcal{A}_d^*$ as a
direct sum of the preduals of the full multiplier algebra and of a commutative
von Neumann algebra, and establish analogues of many classical results
concerning the dual space of the ball algebra. These developments are deeply
intertwined with the problem of peak interpolation 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 $\mathcal{A}^*_d$.
