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A Remark on the Sum of Simultaneously Proximinal Subspaces(PDF)

Journal of Xiamen University(Natural Science)[ISSN:0438-0479/CN:35-1070/N]

Issue:
2017 04
Page:
551-554
Research Field:
Research Articles
Publishing date:
2017-07-26

Info

Title:
A Remark on the Sum of Simultaneously Proximinal Subspaces
Article ID:
0438-0479(2017)04-0551-04
Author(s):
MENG Qingfeng*LUO ZhenghuaSHI Huihua
School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China
Keywords:
proximinal simultaneously proximinal weakly compact sets
CLC number:
O 177.2
DOI:
10.6043/j.issn.0438-0479.201611011
Document code:

A
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.

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Memo

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
Last Update: 1900-01-01