Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 2 (2019), 242-251.
The structure of 2-local Lie derivations on von Neumann algebras
In this article we characterize the form of each 2-local Lie derivation on a von Neumann algebra without central summands of type . We deduce that every 2-local Lie derivation on a finite von Neumann algebra without central summands of type can be written in the form for all in , where is an element in and is a center-valued homogenous mapping which annihilates each commutator of . In particular, every linear 2-local Lie derivation is a Lie derivation on a finite von Neumann algebra without central summands of type . We also show that every 2-local Lie derivation on a properly infinite von Neumann algebra is a Lie derivation.
Ann. Funct. Anal., Volume 10, Number 2 (2019), 242-251.
Received: 15 May 2018
Accepted: 29 August 2018
First available in Project Euclid: 19 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 47B47: Commutators, derivations, elementary operators, etc.
Secondary: 47C15: Operators in $C^*$- or von Neumann algebras
Yang, Bing; Fang, Xiaochun. The structure of 2-local Lie derivations on von Neumann algebras. Ann. Funct. Anal. 10 (2019), no. 2, 242--251. doi:10.1215/20088752-2018-0024. https://projecteuclid.org/euclid.afa/1552960864