This is an announcement for the paper "Boundaries for algebras of holomorphic functions on Banach spaces" by Yun Sung Choi Kwang Hee Han Han Ju Lee.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46E50; 46B20; 46B45

The source file(s), shilovboundary-final-corrected.tex: 39013 bytes, is(are) stored in gzipped form as 0708.4068.gz with size 12kb. The corresponding postcript file has gzipped size 102kb.

Submitted from: hahnju@postech.ac.kr

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