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[1]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(04):551-554.[doi:10.6043/j.issn.0438-0479.201611011]
 MENG Qingfeng*,LUO Zhenghua,SHI Huihua.A Remark on the Sum of Simultaneously Proximinal Subspaces[J].Journal of Xiamen University(Natural Science),2017,56(04):551-554.[doi:10.6043/j.issn.0438-0479.201611011]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
56卷
期数:
2017年04期
页码:
551-554
栏目:
研究论文
出版日期:
2017-07-26

文章信息/Info

Title:
A Remark on the Sum of Simultaneously Proximinal Subspaces
文章编号:
0438-0479(2017)04-0551-04
作者:
孟庆丰*罗正华施慧华
华侨大学数学科学学院,福建 泉州 362021
Author(s):
MENG Qingfeng*LUO ZhenghuaSHI Huihua
School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China
关键词:
可逼近 联合可逼近 弱紧集
Keywords:
proximinal simultaneously proximinal weakly compact sets
分类号:
O 177.2
DOI:
10.6043/j.issn.0438-0479.201611011
文献标志码:
A
摘要:
G是Banach空间X的闭子集.G称为在X中是联合可逼近的(simultaneously proximinal),如果对每个有界集AX,都存在g∈G,使得d(A,G)≡infu∈Gsupa∈A‖a-u‖=supa∈A‖a-g‖.证明了Banach空间中的弱紧凸集与联合可逼近凸集的和是联合可逼近的.作为推论,证明了对于Banach空间X的自反子空间F和联合可逼近子空间G,如果F+G 是闭的,F+G是联合可逼近的.
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∈Aa-u‖=supa∈Aa-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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2016-11-02 录用日期:2016-12-19
基金项目:国家自然科学基金(11201160,11401227); 福建省自然科学基金(2015J05007)
*通信作者:641289221@qq.com
更新日期/Last Update: 1900-01-01