湖北民族学院学报（自然科学版）2016，Vol.34Issue(4)：380-385,6.DOI:10.13501/j.cnki.42-1569/n.2016.12.005
希尔伯特空间的序列弱完备性
Weakly Sequential Completeness of Hilbert Spaces
摘要
Abstract
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.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Key words
inner product space/Hilbert space/weak inner product convergence/weak basic sequence/weak sequential completeness分类
数理科学引用本文复制引用
代兵,艳艳,包玉娥..希尔伯特空间的序列弱完备性[J].湖北民族学院学报（自然科学版）,2016,34(4):380-385,6.基金项目
内蒙古自然科学基金项目(2010MS0119) （2010MS0119）
