Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 18 (2011), No. 4, 1065--1074Copyright Heldermann Verlag 2011 The Biduality Problem and M-Ideals in Weighted Spaces of Holomorphic Functions Christopher Boyd School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland Pilar Rueda Dep. de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjasot, Valencia, Spain [Abstract-pdf] 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. [ Fulltext-pdf  (137  KB)] for subscribers only.