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Biduals of weighted banach spaces of analytic functions

Part of: Topological linear spaces and related structures Linear function spaces and their duals Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

K. D. Bierstedt  and
W. H. Summers
K. D. Bierstedt
Affiliation:
FB 17, MathematikUniversität-GH-PaderbornPostfach 16 21 D-4790 Paderborn, Germany
W. H. Summers
Affiliation:
Department of Mathematical Sciences University of ArkansasFayetteville, AR 72701, U.S.A.
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Abstract

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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 Hν(G) is naturally isometrically isomorphic to Hν0(G)**, and show in particular that this is the case whenever the closed unit ball in Hν0(G) in compact-open dense in the closed unit ball of Hν(G).

MSC classification

Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions 46A70: Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 46B10: Duality and reflexivity
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 70 - 79
Copyright
Copyright © Australian Mathematical Society 1993

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