On Proximinality of Convex Sets in Superspaces

作     者：Li Xin CHENG Zheng Hua LUO Wen ZHANG Ben Tuo ZHENG 

作者机构：School of Mathematical Sciences Xiamen University School of Mathematical Sciences Huaqiao University Department of Mathematical Sciences the University of Memphis 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2016年第32卷第6期

页      面：633-642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 National Natural Science Foundation of China(Grant No.11371296) supported by National Natural Science Foundation of China(Grant No.11201160) supported by National Natural Science Foundation of China(Grant No.11471270) Ph.D Programs Foundation of MEC(Grant No.20130121110032) Natural Science Foundation of Fujian Province(Grant No.2012J05006) Natural Science Foundation of Fujian Province(Grant No.2015J01022) supported by NSF(Grant No.DMS-1200370) 

主　　题：Proximinality convex set local compactness Banach space 

摘      要：Abstract In this paper, we show that a closed convex subset C of a Banach space is strongly proximinal （proximinal, resp.） in every Banach space isometrically containing it if and only if C is locally （weakly, resp.） compact. As a consequence, it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it, the metric projection from Y to C is nonempty set-valued and upper semi-continuous.