数学季刊 ›› 2022, Vol. 37 ›› Issue (1): 52-60.doi: 10.13371/j.cnki.chin.q.j.m.2022.01.005

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  1. School of Mathematics, East China University of Science and Technology
  • 收稿日期:2021-07-08 出版日期:2022-03-30 发布日期:2022-03-30
  • 通讯作者: LI Qi-hui (1978-) female, native of Yinchuan, Ningxia, associative professor of East China University of Science and Technology, engages in functional analysis E-mail: qihui li@126.com
  • 作者简介:ZHAN Xiong-feng (2001-), male, native of Duchang, Jiangxi, undergraduate student of East China University of Science and Technology, engages in functional analysis; RUAN Yi-fei (2001-), male, native of Tongling, Anhui, undergraduate student of East China University of Science and Technology, engages in functional analysis; HUANG He-nan-bei (2000-), male, native of Shijiazhong, Hebei, undergraduate student of East China University of Science and Technology, engages in functional analysis; LI Qi-hui (1978-) female, native of Yinchuan, Ningxia, associative professor of East China University of Science and Technology, engages in functional analysis.
  • 基金资助:

    Supported by the Undergraduate Training Program on Innovation and Entrepreneurship (Grant No. X202110251333);

    National Natural Science Foundation of China (Grant No. 11671133).

Generalized Wave Operators in Von Neumann Algebras

  1. School of Mathematics, East China University of Science and Technology
  • Received:2021-07-08 Online:2022-03-30 Published:2022-03-30
  • Contact: LI Qi-hui (1978-) female, native of Yinchuan, Ningxia, associative professor of East China University of Science and Technology, engages in functional analysis E-mail: qihui li@126.com
  • About author:ZHAN Xiong-feng (2001-), male, native of Duchang, Jiangxi, undergraduate student of East China University of Science and Technology, engages in functional analysis; RUAN Yi-fei (2001-), male, native of Tongling, Anhui, undergraduate student of East China University of Science and Technology, engages in functional analysis; HUANG He-nan-bei (2000-), male, native of Shijiazhong, Hebei, undergraduate student of East China University of Science and Technology, engages in functional analysis; LI Qi-hui (1978-) female, native of Yinchuan, Ningxia, associative professor of East China University of Science and Technology, engages in functional analysis.
  • Supported by:

    Supported by the Undergraduate Training Program on Innovation and Entrepreneurship (Grant No. X202110251333);

    National Natural Science Foundation of China (Grant No. 11671133).

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摘要：

Let M⊆B(H) be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight τ where B(H) is the set of all bounded linear operators on Hilbert space H. The main purpose of this article is to introduce generalized weak wave operators \tide{W}± , generalized weak abelian wave operators \tide{U}± and generalized stationary wave operators U± in M and then to explore the relation among \tide{W}± , \tide{U}± , U± and generalized wave operators W±.

关键词: Generalized wave operators, Von Neumann algebras, Generalized weak wave operators, Generalized stationary wave operators

Abstract: Let M⊆B(H) be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight τ where B(H) is the set of all bounded linear operators on Hilbert space H. The main purpose of this article is to introduce generalized weak wave operators \tide{W}± , generalized weak abelian wave operators \tide{U}± and generalized stationary wave operators U± in M and then to explore the relation among \tide{W}± , \tide{U}± , U± and generalized wave operators W±.

Key words: Generalized wave operators, Von Neumann algebras, Generalized weak wave operators, Generalized stationary wave operators

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