矢值序列空间上的一类无穷矩阵变换  

A Class of Infinite Matrix Transformations on Vector-valued Sequence Space

作　　者：王富彬 金鸿章[1] 李容录[2] 王辉[1] 

机构地区：[1]哈尔滨工程大学自动化学院,哈尔滨150001 [2]哈尔滨工业大学理学院,哈尔滨150001

出　　处：《应用泛函分析学报》2009年第2期184-192,共9页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(50879012);黑龙江省博士后资助经费项目(LBH-Z05059)

摘　　要：对于一类经典的矢值序列空间,文中引入了一类重要子集,它包括了该序列空间的全部全有界集和许多非全有界集.利用Antosik-Mikusinski基本矩阵定理和该子集族,对于一类映射矩阵获得了一个无穷矩阵收敛定理,并且给出了一类经典无穷矩阵变换的更强刻划.此结果补充和完善了非线性矩阵变换定理.For a type of classic vector-valued sequence space, a class of important subsets was introduced in this article, it includes all totally bounded sets and many sets which are not totally bounded in the sequece space. From the Antosik-Mikusinski basic matrix theorem and the subset family, for a type of mapping matrix, an infinite matrix convergence theorem is obtained, and the stronger characterizations of a class of classical infinite matrix transformations were also derived. The conclusions supplement and perfect the nonlinear matrix transformation theorem

关 键 词：一致变差耗尽 一致消失 序列对偶空间 无穷矩阵变换 

分 类 号：O177.2[理学—数学]