关于级数绝对收敛的Orlicz-Pettis型定理  

Orlicz-Pettis Theorem in Absolutely Convergent Series

作　　者：顾娟[1] 张向华[1] 

机构地区：[1]黑龙江科技学院理学院,哈尔滨150027

出　　处：《科技导报》2011年第17期65-67,共3页Science & Technology Review

基　　金：黑龙江省教育厅科学技术研究项目(11541325)

摘　　要：为深入探讨级数的绝对收敛问题,引入一个具有普遍意义的抽象对偶系统(E,F),其中 F哿GE,G 为局部凸空间。在(E,F)上给出级数绝对收敛的定义,讨论子级数收敛与绝对收敛的关系,得到了一个关于级数绝对收敛的 Orlicz-Pettis 型定理。Series convergent is a research fields which has the great significance in functional analysis.In order to study the problem of absolutely convergent series,an abstract duality pair（E,F） which has the universal meaning on the basis of literature [4] was introduced,in the pair,F GE,where G is locally convex space.And then the definition of absolutely convergent series on it was given,the relationship between subseries convergent and absolute convergent was discussed,also a Orlicz-Pettis theorem of absolutely convergent series was obtained,that is,the topology of uniform convergence in every M∈Bop（E,F） has the same absolutely convergent series.Such a conclusion expands the serviceable range of absolute convergence Orlicz-Pettis Theorem,which is very important to the study of absolute convergence theory,and is an effective way to depict the space to a certain extent.

关 键 词：Orlicz-Pettis 拓扑 绝对收敛 序列完备 

分 类 号：O173.1[理学—数学]