Journal of the Australian Mathematical Society (Series A)

Research Article

Biduals of weighted banach spaces of analytic functions

K. D. Bierstedta1 and W. H. Summersa2

a1 FB 17, Mathematik Universität-GH-Paderborn Postfach 16 21 D-4790 Paderborn, Germany

a2 Department of Mathematical Sciences University of Arkansas Fayetteville, AR 72701, U.S.A.

Abstract

For a positive continuous weight function ν on an open subset G of CN, let Hv(G) and Hv0(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that ν f is bounded and ν f vanishes at infinity, respectively. We address the biduality problem as to when (G) is naturally isometrically isomorphic to 0(G)**, and show in particular that this is the case whenever the closed unit ball in 0(G) in compact-open dense in the closed unit ball of (G).

(Received October 31 1990)

(Revised September 02 1991)

1991 Mathematics subject classification (Amer. Math. Soc)

  • 46 E 15;
  • 46 A 70;
  • 46 B 10