Illinois Journal of Mathematics

2-local triple derivations on von Neumann algebras

Karimbergen Kudaybergenov, Timur Oikhberg, Antonio M. Peralta, and Bernard Russo

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Abstract

We prove that every (not necessarily linear nor continuous) 2-local triple derivation on a von Neumann algebra $M$ is a triple derivation, equivalently, the set $\operatorname{Der}_{t}(M)$, of all triple derivations on $M$, is algebraically 2-reflexive in the set $\mathcal{M}(M)=M^{M}$ of all mappings from $M$ into $M$.

Article information

Source
Illinois J. Math., Volume 58, Number 4 (2014), 1055-1069.

Dates
Received: 9 December 2014
Revised: 27 August 2015
First available in Project Euclid: 6 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1446819301

Digital Object Identifier
doi:10.1215/ijm/1446819301

Mathematical Reviews number (MathSciNet)
MR3421599

Zentralblatt MATH identifier
1332.46055

Subjects
Primary: 46L05: General theory of $C^*$-algebras 46L40: Automorphisms

Citation

Kudaybergenov, Karimbergen; Oikhberg, Timur; Peralta, Antonio M.; Russo, Bernard. 2-local triple derivations on von Neumann algebras. Illinois J. Math. 58 (2014), no. 4, 1055--1069. doi:10.1215/ijm/1446819301. https://projecteuclid.org/euclid.ijm/1446819301


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