摘要
研究了Banach空间X中的级数∑∞n=1xn的收敛性、绝对收敛性、弱无条件收敛性、无条件收敛性与可和性等概念之间的关系,证明了:当X为一般Banach空间时,无条件收敛性与可和性是等价的;当X为Hilbert空间时,弱无条件收敛性、无条件收敛性及可和性是等价的;当X为数域时,无条件收敛性与绝对收敛性及可和性是等价的.
It is discussed that the relations between the convergence, absolute convergence, weakly unconditional convergence and unconditional convergence and summability of an infinite series ∑∞n=1x_nin a Banach space X. The following conclusions are proved: (1) In a Banach space X, the unconditional convergence and summability of an infinite series are equivalent; (2) In a Hilbert space X, the weakly unconditional convergence, unconditional convergence and summability of an infinite series are equivalent; (3) In the case X is R or C, the unconditional convergence and absolute convergence as well as summability of an infinite series are equivalent.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2004年第4期15-18,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(19971056)
陕西省自然科学研究计划资助项目(2002A02)
关键词
条件收敛
BANACH空间
等价
绝对收敛
收敛性
无穷级数
注记
证明
一般
概念
Banach space
infinite series
convergence
absolute convergence
weakly unconditional convergence
unconditional convergence
summability
