| 冯·诺依曼代数的可测算子的性质 |
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| 引用本文： | 沈丛丛,蒋立宁,王利广.冯·诺依曼代数的可测算子的性质[J].数学学报,2019,62(2):293-302. |
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| 作者姓名： | 沈丛丛 蒋立宁 王利广 |
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| 作者单位： | 1. 北京物资学院信息学院 北京 101149;
2. 北京理工大学数学与统计学院 北京 100081;
3. 曲阜师范大学数学科学学院 曲阜 273165 |
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| 基金项目： | 国家自然科学基金资助项目（11671133，11371222，11701423，11871303） |
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| 摘 要： | 本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.
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| 关 键 词： | 闭算子 稠定算子 可测算子 阶梯算子 |
Properties of Measurable Operators Associated with a von Neumann Algebra |
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| Cong Cong SHEN,Li Ning JIANG,Li Guang WANG.Properties of Measurable Operators Associated with a von Neumann Algebra[J].Acta Mathematica Sinica,2019,62(2):293-302. |
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| Authors: | Cong Cong SHEN Li Ning JIANG Li Guang WANG |
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| Institution: | 1. School of Information, Beijing Wuzi University, Beijing 101149, P. R. China;
2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China;
3. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China |
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| Abstract: | In this article, some properties of measurable operators associated with a von Neumann algebra are considered. The concept of step operator is defined and it is proved that any positive measurable operator can be strongly approximated by some step operators on its domain, which means that any positive measurable operator can be strongly approximated by some projections on its domain. In addition, the measurability of composition operator of measurable operator and bounded operator is discussed. |
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| Keywords: | closed operator densely defined operator measurable operator step operator |
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