Approximately 2-Local Derivations on the Semi-finite von Neumann Algebras

被引：0
|
作者：
Zhao X. [1 ]
Fang X. [1 ]
Yang B. [1 ]
机构：
[1] School of Mathematical Sciences, Tongji University, Shanghai
来源：
Tongji Daxue Xuebao/Journal of Tongji University | 2019年 / 47卷 / 09期
关键词：
Approximately 2-local derivation; Derivation; Semi-finite von Neumann algebra;
D O I：
10.11908/j.issn.0253-374x.2019.09.016
中图分类号：
学科分类号：
摘要：
The definition of approximately 2-local derivation on von Neumann algebras is introduced based on the definitions of approximately local derivation and 2--local derivation. Approximately 2-local derivations on semi-finite von Neumann algebras are studied. Let M be a von Neumann algebra and Δ: M→M be an approximately 2-local derivation. It is easy to obtain that Δ is homogeneous and Δ satisfies Δ(x2) =Δ(x)x+xΔ(x) for any x∈M. Besides, if M is a von Neumann algebra with a faithful normal semi-finite trace τ, then a sufficient condition for Δ to be additive is given, that is, Δ(Mτ)⊆Mτ, where Mτ={x∈M:τ(|x|)<∞}. In all, if Δ is an approximately 2-local derivation on a semi-finite von Neumann algebra with a faithful normal semi-finite trace τ and satisfies Δ(Mτ)⊆Mτ, where Mτ={x∈M:τ(|x|)<∞}, by the conclusion that the Jordon derivation from a 2-torsion free semi-prime ring to itself is a derivation, it follows that Δ is a derivation. © 2019, Editorial Department of Journal of Tongji University. All right reserved.
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页码：1350 / 1354
页数：4
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