| 矢值序列空间上的一类无穷矩阵变换 |
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| 引用本文： | 王富彬,金鸿章,李容录,王辉. 矢值序列空间上的一类无穷矩阵变换[J]. 应用泛函分析学报, 2009, 11(2): 184-192 |
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| 作者姓名： | 王富彬 金鸿章 李容录 王辉 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，黑龙江省博士后启动基金 |
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| 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．
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| 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 |
A Class of Infinite Matrix Transformations on Vector-valued Sequence Space |
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| WANG Fu-bin,JIN Hong-zhang,LI Rong-lu,WANG Hui. A Class of Infinite Matrix Transformations on Vector-valued Sequence Space[J]. Acta Analysis Functionalis Applicata, 2009, 11(2): 184-192 |
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| Authors: | WANG Fu-bin JIN Hong-zhang LI Rong-lu WANG Hui |
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| Affiliation: | 1. Automation College, Harbin Engineering University, Harbin 150001, China 2. College of Science, Harbin Institute of Technology, Harbin 150001, China) |
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| Abstract: | 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 |
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| Keywords: | unifomly variational exhaustive uniformly vanishing sequential dual space infinite matrix transformation |
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