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近可凹性和Banach空间的逼近紧性及度量投影算子的连续性
引用本文:商绍强,崔云安,付永强.近可凹性和Banach空间的逼近紧性及度量投影算子的连续性[J].中国科学:数学,2011,41(9):815-825.
作者姓名:商绍强  崔云安  付永强
作者单位:哈尔滨工业大学理学院数学系, 哈尔滨 150001;
哈尔滨理工大学应用科学院数学系, 哈尔滨 150080
基金项目:国家自然科学基金(批准号:11061022)和哈尔滨理工大学学科带头人基金资助项目 致谢 作者对审稿人的有益建议深表感谢.
摘    要:本文定义了近可凹的Banach 空间. 利用Banach 空间几何技巧证得: X 是逼近紧的当且仅当(1) X 是近可凹的; (2) X 是近严格凸的. 还证明了如果Banach 空间X 是近可凹的, 则对任意闭凸集C, 度量投影算子PC 是上半连续的. 最后作者给出了近可凹性在广义逆理论中的应用.

关 键 词:近可凹性  逼近紧性  度量投影算子  上半连续  近严格凸性

Nearly dentability and approximative compactness and continuity of metric projector in Banach spaces
SHANG ShaoQiang,CUI YunAn,FU YongQiang.Nearly dentability and approximative compactness and continuity of metric projector in Banach spaces[J].Scientia Sinica Mathemation,2011,41(9):815-825.
Authors:SHANG ShaoQiang  CUI YunAn  FU YongQiang
Institution:SHANG ShaoQiang, CUI YunAn , FU YongQiang
Abstract:In this paper, authors define nearly dentability of Banach space. Authors prove that X is approximatively compact if and only if (1) X is nearly dentable space, and (2) X is nearly strict convex space. By the method of geometry of Banach spaces, authors also prove that if X is nearly dentable space, then for any closed convex subset C, metric projector Pc is upper semicontinuous. Finally, authors give important application of nearly dentability in generalized inverse theory.
Keywords:nearly dentability  approximative compactness  metric projector  upper semicontinuous  nearlystrictly convexity
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