Advances in Operator Theory

2-Local derivations on matrix algebras and algebras of measurable operators

Shavkat Ayupov, Karimbergen Kudaybergenov, and Amir Alauadinov

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Abstract

Let $\mathcal{A}$ be a unital Banach algebra such that any Jordan derivation from $\mathcal{A}$ into any $\mathcal{A}$-bimodule $\mathcal{M}$ is a derivation. We prove that any 2-local derivation from the algebra $M_n(\mathcal{A})$ into $M_n(\mathcal{M})$ $(n \geq 3)$ is a derivation. We apply this result to show that any 2-local derivation on the algebra of locally measurable operators affiliated with a von Neumann algebra without direct abelian summands is a derivation.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 4 (2017), 494-505.

Dates
Received: 8 December 2016
Accepted: 12 July 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431724

Digital Object Identifier
doi:10.22034/aot.1612-1074

Mathematical Reviews number (MathSciNet)
MR3730043

Zentralblatt MATH identifier
06804224

Subjects
Primary: 46L57: Derivations, dissipations and positive semigroups in C-algebras 47B47: Commutators, derivations, elementary operators, etc.
Secondary: 47C15: Operators in $C^*$- or von Neumann algebras 16W25: Derivations, actions of Lie algebras

Keywords
matrix algebra derivation inner derivation 2-local derivation measurable operator

Citation

Ayupov, Shavkat; Kudaybergenov, Karimbergen; Alauadinov, Amir. 2-Local derivations on matrix algebras and algebras of measurable operators. Adv. Oper. Theory 2 (2017), no. 4, 494--505. doi:10.22034/aot.1612-1074. https://projecteuclid.org/euclid.aot/1512431724


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