Ball-covering property of Banach spaces that is not preserved under linear isomorphisms

作     者：CHENG LiXin CHENG QingJin LIU XiaoYan 

作者机构：Department of MathematicsXiamen UniversityXiamen 361005China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2008年第51卷第1期

页      面：143-147页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10471114) 

主　　题：ball-covering isomorphic invariant Gateaux differentiability space Banach space 46B20 46G05 

摘      要：By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.