| Banach空间的p-弱近似性质 |
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| 引用本文： | 李长京,方小春. Banach空间的p-弱近似性质[J]. 数学年刊A辑(中文版), 2015, 36(3): 247-256 |
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| 作者姓名： | 李长京 方小春 |
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| 作者单位： | 山东师范大学数学科学学院, 济南 250014.,通讯作者. 同济大学数学系, 上海 200092. |
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| 基金项目： | 本文受国家自然科学基金 (No.11371279) 和山东省科技攻关项目(No.2014GGH201010)的资助. |
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| 摘 要： | 给出了Banach空间的p-弱近似性质和p-有界弱近似性质的定义,获得了这些性质的一些刻画.利用这些刻画证明了如果一个Banach空间X的对偶空间X~*有p-弱近似性质(或p-有界弱近似性质),则X有p-弱近似性质(或p-有界弱近似性质),在一般情况下反之不成立.
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| 关 键 词： | p-紧集 p-弱近似性质 p-有界弱近似性质 |
p-Weak Approximation Property in Banach Spaces |
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| LI Changjing and FANG Xiaochun. p-Weak Approximation Property in Banach Spaces[J]. Chinese Annals of Mathematics, 2015, 36(3): 247-256 |
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| Authors: | LI Changjing and FANG Xiaochun |
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| Affiliation: | School of Mathematical Sciences, Shandong Normal University, Jinan 250014,China. and Corresponding authour. Department of Mathematics, Tongji University,Shanghai 200092, China. |
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| Abstract: | In this paper, the authours introduce the definitions of the p-weak approximationproperty and the p-bounded weak approximation property in Banach spaces, and derivesome characterizations of these properties. They show that if the dual of a Banach space Xhas the p-weak approximation property (or the p-bounded weak approximation property),then X itself has the p-weak approximation property (or the p-bounded weak approximationproperty). The converse is not true in general. |
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| Keywords: | p-Compact set p-Weak approximation property p-Bounded weakapproximation property |
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