| 无穷维赋范线性空间上单的无界线性算子的存在性 |
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| 引用本文： | 崔秀新. 无穷维赋范线性空间上单的无界线性算子的存在性[J]. 烟台大学学报(自然科学与工程版), 2007, 20(4): 248-249 |
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| 作者姓名： | 崔秀新 |
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| 作者单位： | 烟台大学,数学与信息科学学院,山东,烟台,264005 |
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| 基金项目： | 致谢 衷心感谢李德生教授的帮助. |
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| 摘 要： | 利用Zorn引理证明了任何无穷维赋范线性空间上都存在单的无界线性算子,从而得出Banach空间上的具有闭的零子空间的线性算子未必有界.
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| 关 键 词： | Zorn引理 赋范线性空间 单的无界线性算子 零子空间 |
| 文章编号： | 1004-8820（2007）04-0248-02 |
| 收稿时间： | 2006-05-11 |
| 修稿时间： | 2006-05-11 |
Existence of Unbounded Linear Injector on any Infinite Dimensional Normed Space |
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| CUI Xiu-xin. Existence of Unbounded Linear Injector on any Infinite Dimensional Normed Space[J]. Journal of Yantai University(Natural Science and Engineering edirion), 2007, 20(4): 248-249 |
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| Authors: | CUI Xiu-xin |
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| Affiliation: | School of Mathematics and Informational Science,Yantai University, Yantai 264005, China |
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| Abstract: | By Zorn lemma,it has been proved that there is an unbounded linear injector on any infinite dimensional normed space,therefore it gives that a linear operator which has closed null subspace on Banach space is sometimes unbounded and sometimes bounded. |
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| Keywords: | Zorn lemma linear normed space unbounded linear injector null subspace |
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