Boundaries for algebras of holomorphic functions

被引：14
|
作者：
Moraes, LA
Grados, LR
机构：
[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil
[2] Univ Estadual Ponta Grossa, Dept Matemat, BR-84030900 Ponta Grossa, PR, Brazil
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 281卷 / 02期
关键词：
Banach algebra; boundary; holomorphic functions; complex extreme point; peak point;
D O I：
10.1016/S0022-247X(03)00150-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let A(u) (B-G) be the Banach algebra of all complex valued functions defined on the closed unit ball B-G of a complex Banach space G which are uniformly continuous on B-G and holomorphic in the interior of B-G, endowed with the sup norm. A characterization of the boundaries for An (B-G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A(u)(B-G) is also proved. (C) 2003 Elsevier Science (USA). All rights reserved.
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页码：575 / 586
页数：12
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