Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces

Abstract. We study the relations between boundaries for algebras of holo-morphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic func-tions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the Orlicz-Lorentz sequence space λϕ,w is the Shilov boundary for algebras of holomorphic functions on λϕ,w if ϕ satisfies the δ2-condition. 1. Introduction an