| 闭极大线性子空间正交补的判别及应用 |
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| 引用本文： | 谭福玲,刘冠琦,王玉文.闭极大线性子空间正交补的判别及应用[J].数学的实践与认识,2010,40(1). |
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| 作者姓名： | 谭福玲 刘冠琦 王玉文 |
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| 作者单位： | 1. 黑河学院,数学系,黑龙江,哈尔滨,164300
2. 哈尔滨师范大学,数学科学学院,曾远荣泛函分析研究中心,黑龙江,哈尔滨,150025 |
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| 基金项目： | 国家自然科学基金(10671049); 黑龙江省教育厅科研项目(11544011)资助 |
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| 摘 要： | 继续前面的工作,证得对于赋范线性空间中固定线性子空间成为迫近子空间的充分必要条件.特别的,对于闭极大线性子空间来说,的迫近性等价于的正交可补性.做为其直接推论,给出Banach空间成为自反空间的5个等价条件,其中4个条件为经典结果,一个条件为已有文献中给出的条件,但给出全新的证明.
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| 关 键 词： | 赋范线性空间 闭极大线性子空间 正交可补 迫近集 |
The Criterion and Applications of Orthogonal Complement Closed Maximal Linear Space |
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| TAN Fu-ling,LIU Guan-qi,WANG Yu-wen.The Criterion and Applications of Orthogonal Complement Closed Maximal Linear Space[J].Mathematics in Practice and Theory,2010,40(1). |
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| Authors: | TAN Fu-ling LIU Guan-qi WANG Yu-wen |
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| Institution: | TAN Fu-ling1,LIU Guan-qi2,WANG Yu-wen2(1.Department of Mathematics,Heihe College,Harbin 164300,China)(2.Department of Mathematics,Harbin Normal University,Harbin 150025,China) |
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| Abstract: | We continue the work in relevant reference,prove a necessary and sufficient conditions for criteria of a fixed linear Subspace in normed linear space.Especially,for closed maximal subspace,the criteria of equals to is orthogonal complemented.As a direct inference,we get five equal conditions for Banach space to be a dual space,four of them are classical results,the rest one is a condition got in relevant reference, but we give a new proof. |
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| Keywords: | normed linear space bounded maximal linear subspace orthogonal complement criteria space |
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