Generalized Wave Operators in Von Neumann Algebras

ZHAN Xiong-feng, RUAN Yi-fei, HUANG He-nan-bei, LI Qi-hui

doi:10.13371/j.cnki.chin.q.j.m.2022.01.005

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 1: 52 - 60

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.01.005

Generalized Wave Operators in Von Neumann Algebras

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School of Mathematics, East China University of Science and Technology

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.

Received date: 2021-07-08

Online published: 2022-03-30

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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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

Cite this article

ZHAN Xiong-feng, RUAN Yi-fei, HUANG He-nan-bei, LI Qi-hui . Generalized Wave Operators in Von Neumann Algebras[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(1) : 52 -60 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.005

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