Journal of convex analysis, Tome 18 (2011) no. 4, pp. 1065-1074
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C. Boyd; P. Rueda. The Biduality Problem and M-Ideals in Weighted Spaces of Holomorphic Functions. Journal of convex analysis, Tome 18 (2011) no. 4, pp. 1065-1074. http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a8/
@article{JCA_2011_18_4_JCA_2011_18_4_a8,
author = {C. Boyd and P. Rueda},
title = {The {Biduality} {Problem} and {M-Ideals} in {Weighted} {Spaces} of {Holomorphic} {Functions}},
journal = {Journal of convex analysis},
pages = {1065--1074},
year = {2011},
volume = {18},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a8/}
}
TY - JOUR
AU - C. Boyd
AU - P. Rueda
TI - The Biduality Problem and M-Ideals in Weighted Spaces of Holomorphic Functions
JO - Journal of convex analysis
PY - 2011
SP - 1065
EP - 1074
VL - 18
IS - 4
UR - http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a8/
ID - JCA_2011_18_4_JCA_2011_18_4_a8
ER -
%0 Journal Article
%A C. Boyd
%A P. Rueda
%T The Biduality Problem and M-Ideals in Weighted Spaces of Holomorphic Functions
%J Journal of convex analysis
%D 2011
%P 1065-1074
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a8/
%F JCA_2011_18_4_JCA_2011_18_4_a8
Given a weight $v$ on an open subset $U$ of ${\bf C}^n$, ${\cal H}_v(U)$ (resp. ${\cal H}_{v_o}(U)$) denotes the Banach space of holomorphic functions $f$ on $U$ such that $vf$ is bounded on $U$ (resp. converges to $0$ on the boundary of $U$). We show that ${\cal H}_v(U)$ is canonically isometrically isomorphic to the bidual of ${\cal H}_{v_o}(U)$ if and only if ${\cal H}_{v_o}(U)$ is an M-ideal in ${\cal H}_v(U)$ and the associated weights $\tilde v_o$ and $\tilde v$ coincide.
