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.
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.
出处
《洛阳师范学院学报》
2006年第5期27-28,126,共3页
Journal of Luoyang Normal University
关键词
无穷级数
绝对收敛
无条件收敛
收敛
弱无条件收敛
infinite series
absolute convergence
unconditional convergence
convergence
weakly unconditional convergence
