Weak products of complete pick spaces
Let H be the Drury-Arveson or Dirichlet space of the unit ball of Cd. The weak product H ☉ H of H is the collection of all functions h that can be written as h =∑∞n=1 fngn, where ∑∞n=1 ||fn|| ||gn|| < ∞. We show that H ☉ H is contained in the Smirnov class of H; that is, every function in H ☉ H is a quotient of two multipliers of H, where the function in the denominator can be chosen to be cyclic
