BIDUALS OF WEIGHTED BANACH-SPACES OF ANALYTIC-FUNCTIONS

For a positive continuous weight function v on an open subset G of C(N), let Hv (G) and Hv0(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that vf is bounded and vf vanishes at infinity, respectively. We address the biduality problem as to when Hv(G) is naturally isometrically isomorphic to Hv0(G)**, and show in particular that this is the case whenever the closed unit ball in Hv0(G) is compact-open dense in the closed unit ball of Hv(G) .