局部凸空间中的子级数收敛与绝对收敛  

Subseries convergence and absolute convergence in locally convex spaces

作　　者：杨云燕 李容录[1] 

机构地区：[1]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2006年第3期322-325,共4页Journal of Natural Science of Heilongjiang University

摘　　要：在局部凸空间中建立了级数绝对收敛的概念,并对子级数收敛级数和绝对收敛级数进行了研究,在任意对偶(X,X′)中,找到了拓扑F(C)使得在(X,F(C))中,子级数收敛级数是绝对收敛的.The concept of absolute convergence in locally convex spaces is established. Consider series of sub - series convergent and series of absolutely convergent. For every dual pair （X,X＇）, there exists a topology A L） such that, in （X,A L ）, subseries convergent series are absolutely convergent.

关 键 词：绝对收敛 等度连续 子级数收敛 

分 类 号：O177.3[理学—数学]