摘要
在内积空间中引进一种弱收敛性概念,并研究希尔伯特(Hilbert)空间的序列弱完备性问题.首先,在内积空间中引进了一种序列的弱收敛性——弱内积收敛性概念,并讨论了弱内积收敛序列的有关性质,证明了序列弱内积收敛点的唯一性、弱内积收敛序列的有界性等;其次,在内积空间中引进了弱基本序列及序列弱完备性的概念,并证明了Hilbert空间是序列弱完备空间.
In this paper,we introduce a concept of the weak convergence in the inner product space, and research the problem about the weak sequential completeness of Hilbert space.Firstly,we introduce a con-cept of weak convergence of a sequence in the inner product space,which is called the weak convergence in inner product space.And we discuss the property of weak convergent sequence in inner product space. The properties like the uniqueness of the weakly sequental convergent point in inner product space and the boudedness of weak convergent inner product sequence are proved. Secondly,we introduce the con-cepts of basic weak sequence and weakly sequential completeness,and prove that the Hilbert space is a space whose sequence is weakly complete.
出处
《湖北民族学院学报(自然科学版)》
CAS
2016年第4期380-385,共6页
Journal of Hubei Minzu University(Natural Science Edition)
基金
内蒙古自然科学基金项目(2010MS0119)
关键词
内积空间
HILBERT空间
弱内积收敛
弱基本序列
序列弱完备性
inner product space
Hilbert space
weak inner product convergence
weak basic sequence
weak sequential completeness