大连理工大学主页平台管理系统石瑞--中文主页-- A generalization of Voiculescu's theorem for normal operators to semifinite von Neumann algebras

石瑞教授

石瑞，大连理工大学数学科学学院教授，博士生导师，主要从事泛函分析中算子理论及算子代数相关的研究工作。(α) 主持并参加多项国家自然科学基金;(β) 主要研究兴趣为泛函分析中的算子理论与算子代数。近些年围绕算子代数中的算子理论（如von Neumann代数中正规算子在紧扰动下的对角化、相对不可约算子与可约算子的稠密性等等）以及算子代数的表示理论、分类理论等取得一部分相关研究成果。在《Adv. Math.》、《J. Funct. Anal.》、《J. Noncommut. Geom.》、《SCIENCE CHINA Mathematics》、《Integral Equations Operator Theory》、《Proc. Amer. Math. Soc. 》等学术期刊发表科研论文若干。(γ) 主讲课程：泛函分析、高等数学、...

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A generalization of Voiculescu's theorem for normal operators to semifinite von Neumann algebras

发布时间： 2021-03-05 点击次数：

论文类型：期刊论文
发表刊物：ADVANCES IN MATHEMATICS
卷号：375
页面范围：107347-
ISSN号：0001-8708
关键字：Weyl-von Neumann theorem; Voiculescu's Theorem; Normed ideal; Phi-well-behaved sets; von Neumann algebras
摘要：In this paper, we provide a generalized version of Voiculescu's theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful, normal, semifinite, tracial weight tau, each normal operator is an arbitrarily small (max{parallel to.parallel to, parallel to.parallel to(2)})-norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with a faithful normal semifinite tracial weight, we prove that each self-adjoint operator can be diagonalized modulo normed ideals satisfying a natural condition. An analogue, for nuclear C*-algebras, of Voiculescu's absorption theorem [33, Theorem 2.4] is also proved in the case of semifinite factors. (C) 2020 Elsevier Inc. All rights reserved.
发表时间：2021-01-10

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