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

Abstract

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 $w$ is a radial weight defined on a balanced open subset U of a Banach space $E$.