On irreducible operators in factor von Neumann algebras

被引：2
|
作者：
Wen, Shilin [1 ]
Fang, Junsheng [1 ,2 ]
Shi, Rui [1 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
[2] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050024, Hebei, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 565卷
关键词：
Factor von Neumann algebras; Irreducible operators;
D O I：
10.1016/j.laa.2018.12.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M be a factor von Neumann algebra with separable predual and let T is an element of M. We call T an irreducible operator (relative to M) if W*(T) is an irreducible subfactor of M, i.e., W*(T)' boolean AND M = CI. In this note, we show that the set of irreducible operators in M is a dense G(delta) subset of M in the operator norm. This is a natural generalization of a theorem of Halmos. (C) 2018 Elsevier Inc. All rights reserved.
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页码：239 / 243
页数：5
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