| 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].河海大学学报(自然科学版),2015(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].Journal of Hohai University (Natural Sciences ),2015(3):247-256. |
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| Authors: | LI Changjing and FANG Xiaochun |
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| Institution: | 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 approximation
property and the p-bounded weak approximation property in Banach spaces, and derive
some characterizations of these properties. They show that if the dual of a Banach space X
has 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 approximation
property). The converse is not true in general. |
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| Keywords: | p-Compact set p-Weak approximation property p-Bounded weak
approximation property |
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