| 子空间单位球的逼近紧性 |
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| 引用本文： | 罗正华,孙龙发,陈丽珍.子空间单位球的逼近紧性[J].数学学报,2015,58(6):1045-1052. |
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| 作者姓名： | 罗正华 孙龙发 陈丽珍 |
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| 作者单位： | 1.华侨大学数学科学学院 泉州 362021;2.厦门大学数学科学学院 厦门 361005;3.华侨大学数学科学学院 泉州 362021 |
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| 基金项目： | 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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| 摘 要： | 设X是Banach空间,Y为X的子空间,B_X,B_Y分别是X和Y的闭单位球.本文研究B_Y的逼近紧性,证明了B_Y在X中是逼近紧的当且仅当对Y的每个与B_X相交的平移Y_T,Y_T∩B_X在Y_T中都是逼近紧的.还得到B_Y逼近紧的稳定性结果.
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| 关 键 词： | 逼近紧性 子空间 闭单位球 |
The Approximative Compactness of the Closed Unit Ball of a Subspace in a Banach Space |
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| Zheng Hua LUO,Long Fa SUN,Li Zhen CHEN.The Approximative Compactness of the Closed Unit Ball of a Subspace in a Banach Space[J].Acta Mathematica Sinica,2015,58(6):1045-1052. |
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| Authors: | Zheng Hua LUO Long Fa SUN Li Zhen CHEN |
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| Institution: | 1.School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China;2.School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China;3.School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China |
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| 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 YT ∩ BX ≠ ?, YT ∩ BX is approximative compact in YT . We also obtain the stability result of the approximative compactness of BY. |
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| Keywords: | approximative compactness subspace closed unit ball |
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