Spaces of holomorphic functions on non-balanced domains

This paper studies the coincidence of the τ ω and τ δ topologies on the space of holomorphic functions defined on an open subset U of a Banach space. Dineen and Mujica proved that τ ω = τ δ when U is a balanced open subset of a separable Banach space with the bounded approximation property. Here, we study the τ ω = τ δ problem for several types of non-balanced domains U.