Characterizations of approximation properties determined by operator ideals in the predual weighted spaces of holomorphic functions

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 $E$.