一类矢值序列空间上的矩阵变换定理

摘要

For a type of classical vector-valued sequence space, a class of important subsets was introduced in this article, it includes all bounded sets and many sets which are not 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 stronger characterization of a class of classical infinite matrix transformations was also derived. The results improved the theorem for the sequential evaluation convergence of operator series.%对于一类经典的矢值序列空间,文中引入一类重要子集,它包括了该序列空间的全部有界集和许多非有界集.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,并且给出了一类经典无穷矩阵变换的更强刻画,此结果改进了算子级数序列赋值收敛定理.