| 完备赋范空间中无穷级数的收敛判别法 |
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| 引用本文： | 刘华,习长新.完备赋范空间中无穷级数的收敛判别法[J].湖州职业技术学院学报,2008,6(1):26-28. |
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| 作者姓名： | 刘华 习长新 |
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| 作者单位： | 荆楚理工学院,计算机学院,湖北,荆门,448000 |
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| 摘 要： | 描述在线性赋范空间中无穷级数的收敛，绝对收敛的定义，重点讨论在Banach空间中无穷级数的收敛判别法，证明了当X为一般Banach空间时，无穷级数∑i=1^∞ xi有类似于正项级数的收敛判翔法．
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| 关 键 词： | 赋范空间 Banach空间 无穷级数 收敛 |
| 文章编号： | 1672-2388(2008)01-0026-03 |
| 修稿时间： | 2006年3月7日 |
The Judging Method on Convergence of the Infinite Series in Banach-space |
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| LIU Hua,XI Chang-xin.The Judging Method on Convergence of the Infinite Series in Banach-space[J].Journal of Huzhou Vocational and Technological College,2008,6(1):26-28. |
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| Authors: | LIU Hua XI Chang-xin |
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| Institution: | LIU Hua, XI Chang - xin (The Compute College, Jingchu Science and Engineering College, Jingmen 448000, China) |
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| Abstract: | We introduce the definition of the convergence in the paper,the absolute convergence in the Banach - space. We discuss the judging method on convergence of the infinite series in the Banach - space in detail The following conclusions are proved： the infinite series in Banach - space and series of the positive term are equivalent. |
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| Keywords: | norm space banach- space the infinite series convergence |
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