Boundaries for algebras of holomorphic functions on Banach spaces

Yun Sung Choi, Kwang Hee Han, Han Ju Lee

Published 2007-08-30Version 1

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 $\lambda_{\phi, w}$ is the Shilov boundary for algebras of holomorphic functions on $\lambda_{\phi, w}$ if $\phi$ satisfies the $\delta_2$-condition.