厦门大学学报（自然科学版）2017，Vol.56Issue(4)：551-554,4.DOI:10.6043/j.issn.0438-0479.201611011
关于联合可逼近子空间和的一个注记
A Remark on the Sum of Simultaneously Proximinal Subspaces
摘要
Abstract
Let G be a closed subset of a Banach space X.Then G is said to be simultaneously proximinal in X if, for every bounded set A()X,there exists a g∈G such that d(A,G)≡infu∈G supa∈A ‖a-u‖=supa∈A ‖a-g‖.In this paper,we prove that,if C and D are two convex subsets of a Banach space X,where one is weakly compact and the other is simultaneously proximinal,then C+D is simultaneously proximinal.As a consequence,we prove that if F and G are respectively reflexive subspace and simultaneously proximinal subspace of a Banach spaces X such that F+G is closed,then F+G is simultaneously proximinal.关键词
可逼近/联合可逼近/弱紧集Key words
proximinal/simultaneously proximinal/weakly compact sets分类
数理科学引用本文复制引用
孟庆丰,罗正华,施慧华..关于联合可逼近子空间和的一个注记[J].厦门大学学报（自然科学版）,2017,56(4):551-554,4.基金项目
国家自然科学基金(11201160,11401227) （11201160,11401227）
福建省自然科学基金(2015J05007) （2015J05007）
