子空间单位球的逼近紧性

罗正华, 孙龙发, 陈丽珍

数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 1045-1052.

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数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 1045-1052. DOI: 10.12386/A2015sxxb0103
论文

子空间单位球的逼近紧性

    罗正华1, 孙龙发2, 陈丽珍3
作者信息 +

The Approximative Compactness of the Closed Unit Ball of a Subspace in a Banach Space

    Zheng Hua LUO1, Long Fa SUN2, Li Zhen CHEN3
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文章历史 +

摘要

X是Banach空间, YX的子空间, BX,BY分别是XY的闭单位球. 本文研究BY的逼近紧性,证明了BYX中是逼近紧的当且仅当对Y的每个与BX相交的平移YT,YTBXYT中都是逼近紧的.还得到B_Y逼近紧的稳定性结果.

Abstract

Let Y be a subspace of a Banach space X, BX,BY be the closed unit ball of X and Y respectively. We investigate the approximative compactness of BY. We prove that BY is approximative compact in X if and only if for every translation YT of Y with YTBX ≠ ∅, YTBX is approximative compact in YT . We also obtain the stability result of the approximative compactness of BY.

关键词

逼近紧性 / 子空间 / 闭单位球

Key words

approximative compactness / subspace / closed unit ball

引用本文

导出引用
罗正华, 孙龙发, 陈丽珍. 子空间单位球的逼近紧性. 数学学报, 2015, 58(6): 1045-1052 https://doi.org/10.12386/A2015sxxb0103
Zheng Hua LUO, Long Fa SUN, Li Zhen CHEN. The Approximative Compactness of the Closed Unit Ball of a Subspace in a Banach Space. Acta Mathematica Sinica, Chinese Series, 2015, 58(6): 1045-1052 https://doi.org/10.12386/A2015sxxb0103

参考文献

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基金

国家自然科学基金(11201160,11326112,11401227);福建省自然科学基金(2012J05006,2015J05007)

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