Spaces of holomorphic functions on non-balanced domains

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