冯·诺依曼代数的可测算子的性质

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冯·诺依曼代数的可测算子的性质沈丛丛^1,2, 蒋立宁², 王利广³1. 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 Properties of Measurable Operators Associated with a von Neumann Algebra Cong Cong SHEN^1,2, Li Ning JIANG², Li Guang WANG³1. 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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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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收稿日期: 2018-06-04

MR (2010):

O177.5

基金资助:国家自然科学基金资助项目（11671133，11371222，11701423，11871303）

通讯作者:蒋立宁,E-mail:jianglining@bit.edu.cnE-mail: jianglining@bit.edu.cn

作者简介: 沈丛丛,E-mail:shcc881111@163.com;王利广,E-mail:wangliguang0510@163.com

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. Cong Cong SHEN, Li Ning JIANG, Li Guang WANG. Properties of Measurable Operators Associated with a von Neumann Algebra. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 293-302.

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