ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1912-1920.

ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES

董云柏¹, 林培基², 郑本拓²

1 Research Center of Nonlinear Science and School of Mathematics and Computer, Wuhan Textile University, Wuhan 430073, China;
2 Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152-3240, USA

收稿日期:2017-03-31 修回日期:2018-02-18 出版日期:2018-12-25 发布日期:2018-12-28
通讯作者: Yunbai DONG E-mail:baiyunmu301@126.com
作者简介:Pei-Kee LIN,E-mail:pklin@memphis.edu;Bentuo ZHENG,E-mail:bzheng@memphis.edu
基金资助:
Yunbai Dong's research was supported in part by the NSFC (11671314) and the Foundation of Hubei Provincial Department of Education (Q20161602). Bentuo Zheng's research was supported in part by the NSF-DMS (1200370) and the NSFC (11628102).

ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES

Yunbai DONG¹, Pei-Kee LIN², Bentuo ZHENG²

1 Research Center of Nonlinear Science and School of Mathematics and Computer, Wuhan Textile University, Wuhan 430073, China;
2 Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152-3240, USA

Received:2017-03-31 Revised:2018-02-18 Online:2018-12-25 Published:2018-12-28
Contact: Yunbai DONG E-mail:baiyunmu301@126.com
Supported by:
Yunbai Dong's research was supported in part by the NSFC (11671314) and the Foundation of Hubei Provincial Department of Education (Q20161602). Bentuo Zheng's research was supported in part by the NSF-DMS (1200370) and the NSFC (11628102).

摘要/Abstract

摘要： In this article, we study the preservation properties of (Šilov) boundary of multiplicative subgroups in C(X) spaces for non-surjective norm-preserving multiplicative maps. We also show a sufficient condition for surjective maps between groups of positive continuous functions to be a composition operator.

关键词: Banach-Stone theorem, Šilov boundary, composition operator

Abstract: In this article, we study the preservation properties of (Šilov) boundary of multiplicative subgroups in C(X) spaces for non-surjective norm-preserving multiplicative maps. We also show a sufficient condition for surjective maps between groups of positive continuous functions to be a composition operator.

Key words: Banach-Stone theorem, Šilov boundary, composition operator

董云柏, 林培基, 郑本拓. ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES[J]. 数学物理学报(英文版), 2018, 38(6): 1912-1920.

Yunbai DONG, Pei-Kee LIN, Bentuo ZHENG. ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1912-1920.

参考文献

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ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES

ON BANACH-STONE TYPE THEOREMS IN UNIFORM MULTIPLICATIVE SUBGROUPS OF C(K)-SPACES

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