| 平移空间的线性结构 |
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| 引用本文： | 王国俊,白永成.平移空间的线性结构[J].数学学报,2005,48(1):1-10. |
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| 作者姓名： | 王国俊 白永成 |
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| 作者单位： | 陕西师范大学数学研究所，陕西理工学院教学系 西安 710062，西安交通大学基础科学研究中心 西安 710049，汉中 723001 |
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| 基金项目： | 国家自然科学基金重点资助项目(10331010) |
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| 摘 要： | 本文证明了在平移空间上可利用距离在一定条件下构作出线性结构,引入了次范整线性空间的概念,还证明了平移空间是次范整线性空间当且仅当它的平移群是Abel群.泛函分析学中的有界线性算子定理,Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中.
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| 关 键 词： | 平移空间 次范整线性空间 Hahn-Banach定理 |
Linear Structure on Translation Spaces |
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| Guo Jun WANGInstitute of Mathematics,Shaanxi Normal University,Xi'an ,P. R. ChinaScience Research Center,Xi'an Jiaotong University,Xi'an ,P. R. ChinaE-mail: gjwang@snnu.edu.cnYong Cheng BAI.Linear Structure on Translation Spaces[J].Acta Mathematica Sinica,2005,48(1):1-10. |
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| Authors: | Guo Jun WANGInstitute of Mathematics Shaanxi Normal University Xi'an P R ChinaScience Research Center Xi'an Jiaotong University Xi'an P R ChinaE-mail: gjwang@snnueducnYong Cheng BAI |
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| Institution: | Guo Jun WANGInstitute of Mathematics, Shaanxi Normal University, Xi'an 710062, P. R. ChinaScience Research Center, Xi'an Jiaotong University, Xi'an 710049, P. R. ChinaE-mail: gjwang@snnu.edu.cnYong Cheng BAI Department of Mathematics, Shaanxi University of Technology, Hanzhong 723001, P. R. China |
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| Abstract: | It is proved that linear structures can be constructed by means of metrics on translation spaces under certain conditions. The concept of sub-normed Z-linear spaces is introduced and it is clarified that a translation space is a sub-normed Z-linear space if and only if its translation group is Abelian. Analogues the bounded linear operator theorem, the Hahn-Banach theorem and the resonance theorem are established in sub-normed Z-linear space. |
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| Keywords: | Translation space Sub-normed Z-linear space Hahn-Banach theorem |
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