## Illinois Journal of Mathematics

### Boundaries for algebras of holomorphic functions on Banach spaces

#### 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 $S_X$ if $X$ is locally c-convex. In particular, it is shown that the unit sphere of the Orlicz-Lorentz sequence space $\lambda_{\varphi, w}$ is the Shilov boundary for algebras of holomorphic functions on $\lambda_{\varphi, w}$ if $\varphi$ satisfies the $\delta_2$-condition.

#### Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 883-896.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258131108

Digital Object Identifier
doi:10.1215/ijm/1258131108

Mathematical Reviews number (MathSciNet)
MR2379728

Zentralblatt MATH identifier
1214.46033

#### Citation

Choi, Yun Sung; Han, Kwang Hee; Lee, Han Ju. Boundaries for algebras of holomorphic functions on Banach spaces. Illinois J. Math. 51 (2007), no. 3, 883--896. doi:10.1215/ijm/1258131108. https://projecteuclid.org/euclid.ijm/1258131108