强可逼近集的和  

On the Sum of Strongly Proximinal Sets

作　　者：孙龙发[1] 罗正华[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《厦门大学学报（自然科学版）》2013年第3期312-315,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金项目(11201160);福建省自然科学基金项目(2012J05006)

摘　　要：设X是无限维Banach空间,首先证明了X中存在两个强可逼近集A,B,满足A+B不是可逼近的;其次利用紧性证明了X中的紧集与强可逼近集的和是强可逼近的,以及X的有限维子空间与强可逼近子空间的和是强可逼近的.这推广了经典的可逼近集(相应地,可逼近子空间)的和理论.Let X be an infinite-dimensional Banach space,it＇s first showed that there exist two strongly proximinal sets A and B of X satisfying A＋B is closed hut not proximinal. By using compactness it is proved that the sum of a compact set and a strongly proximi- nal set of X is strongly proximinal, and the sum of a finite-dimensional subspace of X and a strongly proximinal subspace of X is strongly proximinal. This generalized the classical theory on the sum of the proximinal sets（respectively, proximinal subspaces）.

关 键 词：可逼近集 强可逼近集 紧集 有限维子空间 

分 类 号：O177.2[理学—数学]