Boundaries for algebras of holomorphic functions on Banach spaces

Abstract

We study the relations between boundaries for algebra's of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere S-x if X is locally c-convex. In particular, it is shown that the unit sphere of the Orlicz-Lorentz sequence space lambda phi,w, is the Shilov boundary for algebras of holomorphic functions on lambda phi,w if phi satisfies the delta(2)-condition.