Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1912-1920.

• Articles • Previous Articles     Next Articles

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

Yunbai DONG1, Pei-Kee LIN2, Bentuo ZHENG2   

  1. 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).

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

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