| AM-紧算子的控制性质 |
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| 引用本文： | 王绍新,陈滋利.AM-紧算子的控制性质[J].信阳师范学院学报(自然科学版),2007,20(1):14-16. |
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| 作者姓名： | 王绍新 陈滋利 |
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| 作者单位： | 西南交通大学,数学系,四川,成都,610031 |
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| 基金项目： | 四川省科技厅基础研究项目 |
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| 摘 要： | 不变子空间问题是算子理论中一个著名的问题,为了把Abramovich等人关于紧算子的不变子空间相关结果推广到AM-紧算子,本文对Banach格上AM-紧算子的性质做了比较深入的探讨.主要研究了其控制性质与格性质,并给出结果:若Banach格E上算子T、S满足0≤S≤T,T是AM-紧算子,则S2是AM-紧算子,AM-紧算子的一些其他性质也进行了相关讨论.
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| 关 键 词： | Banach格 AM-紧算子 控制性质 格性质 |
| 文章编号： | 1003-0972（2007）01-0014-03 |
| 收稿时间： | 2006-06-21 |
| 修稿时间： | 2006-06-212006-09-30 |
The Properties of AM-compact Operators |
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| WANG Shao-xin,CHEN Zi-li.The Properties of AM-compact Operators[J].Journal of Xinyang Teachers College(Natural Science Edition),2007,20(1):14-16. |
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| Authors: | WANG Shao-xin CHEN Zi-li |
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| Institution: | College of Math. , Southwest Jiaotong University, Chengdu 610031, China |
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| Abstract: | The Invariant Subspace Problem is a famous problem in the operator theory.For generalizing the results in Abramovich's paper about the positive compact operators,this paper is devoted to the properties of AM-compact operators on Banach lattice.Its domination and lattice property is given,and it is proven that if a positive operator on a Banach lattice is dominated by an AM-compact operator,then its square is also an AM-compact operator.Some relative properties are also discussed. |
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| Keywords: | Banach lattice AM-compact operator domination property lattice property |
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