Geodesic
The Biduality Problem and M-Ideals in Weighted Spaces of Holomorphic Functions
Journal of convex analysis, Tome 18 (2011) no. 4, pp. 1065-1074

Voir la notice de l'article provenant de la source Heldermann Verlag

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. 
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     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},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a8/}
}
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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/