| 一类矢值序列空间上的矩阵变换定理 |
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| 引用本文： | 王富彬,金鸿章,李容录,王宝玲. 一类矢值序列空间上的矩阵变换定理[J]. 数学进展, 2011, 0(2) |
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| 作者姓名： | 王富彬 金鸿章 李容录 王宝玲 |
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| 作者单位： | 哈尔滨工程大学自动化学院;哈尔滨工业大学理学院; |
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| 基金项目： | 国家自然科学基金(No.50879012) |
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| 摘 要： | 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.
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| 关 键 词： | 本性有界 全有界 序列对偶空间 无穷矩阵变换 |
The Matrix Transformation Theorem on a Type of Vector-valued Sequence Space |
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| WANG Fubin,JIN Hongzhang,LI Ronglu,WANG Baoling. The Matrix Transformation Theorem on a Type of Vector-valued Sequence Space[J]. Advances in Mathematics(China), 2011, 0(2) |
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| Authors: | WANG Fubin JIN Hongzhang LI Ronglu WANG Baoling |
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| Affiliation: | WANG Fubin~1,JIN Hongzhang~1,LI Ronglu~2,WANG Baoling~2 (1.Automation College,Harbin Engineering Univ.,Harbin,Heilongjiang,150001,P.R.China,2.College of Science,Harbin Institute of Technology,P.R.China) |
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| Abstract: | 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 ope... |
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| Keywords: | essentially bounded totally bounded sequential dual space infinite matrix transformation |
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