| 序极限算子的分解 |
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| 引用本文： | 周玉莎,陈滋利,文永明.序极限算子的分解[J].西南民族大学学报(自然科学版),2015,41(3):360-363. |
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| 作者姓名： | 周玉莎 陈滋利 文永明 |
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| 作者单位： | 西南交通大学 数学学院,西南交通大学 数学学院,西南交通大学 数学学院 |
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| 摘 要： | 给出了序极限算子的定义以及其序列的等价刻画,同时得到了当值域空间与定义域空间相同时,序极限算子与区间是极限集是等价的.序极限算子满足左乘的性质,并且由序极限算子构成的全体是闭子空间.除此之外,也给出了判定序极限算子的充分不必要条件,并给出结论不是充要条件的反例.序极限算子具有分解性,即可以通过具有序连续范数的Banach格分解,可得到相关结论.
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| 关 键 词： | 序极限算子 序连续范数 分解性 |
| 收稿时间： | 2014/11/14 0:00:00 |
| 修稿时间： | 2015/1/13 0:00:00 |
The Factorization of Order Limited Operators |
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| Zhou Yu-sh,Chen Zi-li and Weng Yong-ming.The Factorization of Order Limited Operators[J].Journal of Southwest University for Nationalities(Natural Science Edition),2015,41(3):360-363. |
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| Authors: | Zhou Yu-sh Chen Zi-li and Weng Yong-ming |
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| Institution: | Department of Mathematic,Southwest Jiaotong University,Department of Mathematic,Southwest Jiaotong University,Department of Mathematic,Southwest Jiaotong University |
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| Abstract: | In this paper we give the definition and characterization of order limited operator. Also, we discuss the basic properties of order limited operators, that is, the set of all order limited operators from Banach Lattice to Banach space is a norm closed vector subspace. Additionally, we prove that every continuous operator from Banach Lattice to Banach space is order limited operator, but it is not necessary and sufficient. We also obtain the factorization theorem of order limited operator through Banach lattice with order continuous norm and related results. |
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| Keywords: | Order limited operator order continuous norm factorization |
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