一类收敛序列空间上的无穷矩阵变换  

Infinite matrix transformations on a class of convergent sequence spaces

作　　者：王富彬[1] 李荣录[1] 钟叔慧[1] 

机构地区：[1]哈尔滨工业大学数学系

出　　处：《黑龙江大学自然科学学报》2008年第2期166-169,177,共5页Journal of Natural Science of Heilongjiang University

摘　　要：对于Banach空间上的一类经典向量序列空间,确定了一类重要的子集称为一致收敛子集,它包括了该序列空间的全部全有界集及许多非全有界集。利用Antosik-Mikusinski基本矩阵定理和该子集族,对于一类映射矩阵,获得了一系列矩阵变换定理,并且给出了一类无穷矩阵变换的刻划,补充和完善了非线性矩阵变换定理。For a type of classic vector - valued sequence space on Banach space, a class of important subsets is determined and is named uniformly convergent subset. It includes all totally bounded sets and many sets which are not totally bounded in the sequence space. Using Antosik - Mikusinski basic matrix theorem？ and the subset family, for a type of mapping matrix, a series of matrix transformation theorems is obtained, and the characterizations of a class of infinite matrix transformations is also derived. The conclusions are complements and improvements of nonlinear matrix transformation theorem.

关 键 词：收敛序列空间 一致收敛子集 Antosik-Mikusinski基本矩阵定理 无穷矩阵变换 

分 类 号：O177.3[理学—数学]