| 李长京,方小春.Banach 空间的p-弱近似性质[J].数学年刊A辑,2015,36(3):247~256 |
| Banach 空间的p-弱近似性质 |
| p-Weak Approximation Property in Banach Spaces |
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| DOI： |
| 中文关键词: p-紧集, p-弱近似性质, p-有界弱近似性质 |
| 英文关键词:p-Compact set, p-Weak approximation property, p-Bounded weak
approximation property |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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