Weighted spaces of holomorphic functions and sequence spaces

Abstract

Our aim in this note is twofold. Firstly we show that, given any Köthe echelon space of order one, a weighted limit of Banach spaces of holomorphic functions on the disc can be constructed such that the strong dual of the sequence space is isomorphic to a complemented subspace of the projective hull associated with the weighted inductive limit. It is also proved that, under some mild assumptions, a weighted inductive limit of spaces of holomorphic functions is a $(DFS)$- space (and hence the projective description holds) if and only if the associated weights satisfy the condition $(S)$ of Bierstedt, Meise and Summers.