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.
Citation
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
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