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arXiv · 1702.07629

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

Shavkat Ayupov·Karimbergen Kudaybergenov·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.

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Shavkat Ayupov, Karimbergen Kudaybergenov, Amir Alauadinov. 2017-02-24. 2-Local derivations on matrix algebras and algebras of measurable operators. https://arxiv.org/abs/1702.07629

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