一类无穷矩阵变换的刻划  

Characterizations of a Class of Infinite Matrix Transformations

作　　者：王富彬 金鸿章[1] 王辉[2] 

机构地区：[1]哈尔滨工程大学自动化学院,黑龙江哈尔滨150001 [2]哈尔滨师范大学数学系,黑龙江哈尔滨150025

出　　处：《数学的实践与认识》2010年第4期202-210,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(50879012);黑龙江省自然科学基金(TA2005-19)

摘　　要：对于一类经典的矢值序列空间,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,获得了一个无穷矩阵收敛定理,进而给出了一类经典无穷矩阵变换的刻划.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 sequence space.From the Antosik-Mikusinski basic matrix theorem and the subset family, an infinite matrix convergence theorem was obtained and the characterization of a class of classical infinite matrix transformations was also derived.

关 键 词：一致耗尽 全有界 序列对偶空间 无穷矩阵变换 

分 类 号：O151.21[理学—数学]