| ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE |
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| 引用本文： | 杨长森. ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE[J]. 数学物理学报(B辑英文版), 2003, 23(3): 351-355. DOI: 10.1016/S0252-9602(17)30342-9 |
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| 作者姓名： | 杨长森 |
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| 作者单位： | Department of |
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| 基金项目： | Natural Science and Education Foundationof Henan Province and Young Fundation of Henan Normal University |
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| 摘 要： | Let X be a Banach space and {e_j}_(j=1)~∞ be a sequence in X. The author showsthat {e_j}_(j=1)~∞ is a basic sequence if and only if ∑_(n=1)~∞, r_nα_(nj) converges for every j≥1 and∑_(n=1)~∞ r_n ∑_(j=1)~∞, α_(nj)e_j=∑_(j=1)~∞,(∑_(n=1)~∞ r_nα_(nj))e_j holds for every choice of scalar variables{α_(nj)} such that ∑_(j=1)~∞ α_(nj)e_j converges for each n≥1 and any choice of scalar variables{r_n} such that ∑_(n=1)~∞ ∑_(j=1)~∞, r_nα_(nj)e_j converges. Moreover, some applications about theresult are given.
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| 收稿时间： | 2001-04-16 |
ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE |
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| Yang Changsen. ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE[J]. Acta Mathematica Scientia, 2003, 23(3): 351-355. DOI: 10.1016/S0252-9602(17)30342-9 |
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| Authors: | Yang Changsen |
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| Affiliation: | Yang Changsen Department of Mathematics,Henan Normal University,Xinxiang 453002,China |
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| Abstract: | |
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| Keywords: | Basic sequence multiple series |
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