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Autumn 2017 2-Local derivations on matrix algebras and algebras of measurable operators
Shavkat Ayupov, Karimbergen Kudaybergenov, Amir Alauadinov
Adv. Oper. Theory 2(4): 494-505 (Autumn 2017). DOI: 10.22034/aot.1612-1074

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.

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Shavkat Ayupov. Karimbergen Kudaybergenov. Amir Alauadinov. "2-Local derivations on matrix algebras and algebras of measurable operators." Adv. Oper. Theory 2 (4) 494 - 505, Autumn 2017. https://doi.org/10.22034/aot.1612-1074

Information

Received: 8 December 2016; Accepted: 12 July 2017; Published: Autumn 2017
First available in Project Euclid: 4 December 2017

zbMATH: 06804224
MathSciNet: MR3730043
Digital Object Identifier: 10.22034/aot.1612-1074

Subjects:
Primary: 46L57, 47B47
Secondary: 16W25, 47C15

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.2 • No. 4 • Autumn 2017
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