J Austral Math Soc Ser A 54 pp70--79, 1993.

Biduals of Weighted Banach Spaces of Analytic Functions

K. D. Bierstedt and W. H. Summers

(Received 31 October 1990; revised 2 September 1991)

Abstract

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).

1991 AMS Subject Classification: 46E15, 46A70, 46B10

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Authors

K. D. Bierstedt: FB 17, Mathematik, Universität-GH-Paderborn, Postfach 16 21, D-4790 Paderborn, Germany.
W. H. Summers: Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, U.S.A.

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