Boundaries for algebras of holomorphic functions on Banach spaces

Yun Sung Choi, Kwang Hee Han, Han Ju Lee

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

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 languageEnglish
Pages (from-to)883-896
Number of pages14
JournalIllinois Journal of Mathematics
Volume51
Issue number3
DOIs
StatePublished - 2007

Keywords

  • Banach sequence space
  • Boundary for algebra
  • Complex convexity
  • Local uniform monotonicity
  • Shilov boundary

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