Abstract
We study the relations between boundaries for algebras 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 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.
Original language | English |
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Pages (from-to) | 883-896 |
Number of pages | 14 |
Journal | Illinois Journal of Mathematics |
Volume | 51 |
Issue number | 3 |
DOIs | |
State | Published - 2007 |
Keywords
- Banach sequence space
- Boundary for algebra
- Complex convexity
- Local uniform monotonicity
- Shilov boundary