  In this article, we show that the predual $\mathcal{G}_w(U)$ of the weighted
space of holomorphic functions has the $\mathcal{I}$- approximation property if
and only if $E$ has the $\mathcal{I}$- approximation property, where
$\mathcal{I}$ is a suitably chosen operator ideal, and $\it{w}$ is a radial
weight defined on a balanced open subset U of a Banach space $E$.
