Banach空间中级数弱无条件收敛性的若干等价刻画  

Equivalent Characterizations of Weak Unconditional Convergence of Infinite Series in Banach Spaces

作　　者：李瑶 卢霁萌 LI Yao;LU Jimeng(School of Mathematics,Tianjin University,Tianjin 300350,China;School of Mathematical Sciences,Nankai University,Tianjin 300071,China)

机构地区：[1]天津大学数学学院,天津300072 [2]南开大学数学科学学院,天津300071

出　　处：《重庆理工大学学报（自然科学）》2021年第3期230-236,共7页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(51877144)。

摘　　要：阐述了范数拓扑下赋范空间中无穷级数的无条件收敛性、子列收敛性、有界乘子收敛性、重排收敛性和符号收敛性及对应的Cauchy性质的定义及其之间的关系,回顾了级数绝对收敛性与无条件收敛性的关系,阐述了上述5种收敛性在弱拓扑下的Banach空间中的定义,给出了其相互关系的完整证明,比较了与范数拓扑下的异同。In the case of Banach spaces under norm topology,definitions of unconditional convergence,subseries convergence,bounded multiplier convergence,reordered convergence and sign convergence and the corresponding Cauchy properties of infinite series were stated.The relationship among the convergences above and the relationship between unconditional convergence and absolute convergence were revisited.The counterparts of the five convergences in Banach spaces under weak topology were provided,as well as a complete proof of their relationship.Similarities of and differences between norm and weak topology were compared.

关 键 词：BANACH空间 无穷级数 Cauchy条件 弱拓扑 弱无条件收敛性 

分 类 号：O177[理学—数学]