| Banach空间中无穷级数收敛性问题 |
| |
| 引用本文： | 董立华,尹秀玲,刘莉. Banach空间中无穷级数收敛性问题[J]. 洛阳师范学院学报, 2006, 25(5): 27-28,126 |
| |
| 作者姓名： | 董立华 尹秀玲 刘莉 |
| |
| 作者单位： | 德州学院数学系,山东德州,253023 |
| |
| 摘 要： | 文中讨论了无穷维赋范线性空间中,级数的收敛、绝对收敛、条件收敛、无条件收敛、弱无条件收敛等概念之间的关系,且通过反例说明弱无条件收敛的级数未必收敛、无条件收敛的级数未必绝对收敛等重要结论.
|
| 关 键 词： | 无穷级数 绝对收敛 无条件收敛 收敛 弱无条件收敛 |
| 文章编号： | 1009-4790（2006）05-0027-02 |
| 收稿时间： | 2006-04-07 |
| 修稿时间： | 2006-04-07 |
The Problem of Convergence of Infinite Series in Banach Space |
| |
| DONG Li-hua,YIN Xiu-ling,LIU Li. The Problem of Convergence of Infinite Series in Banach Space[J]. Journal of Luoyang Teachers College, 2006, 25(5): 27-28,126 |
| |
| Authors: | DONG Li-hua YIN Xiu-ling LIU Li |
| |
| Abstract: | In normed space with limited dimension and infinite dimensional Fréche space,unconditional convergence of series is equivalent with absolute convergence.This paper discusses the relations of several concepts such as convergence,absolute convergence,conditional convergence,unconditional convergence and weak unconditional convergence of series in normed spaces with infinite dimension.And using some counterexamples we explained the important conclusions that weakly unconditional convergent series is unnecessary convergent and unconditional convergent series is unnecessary absolute convergent. |
| |
| Keywords: | infinite series absolute convergence unconditional convergence convergence weakly unconditional convergence |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
