Ayupov, S., Kudaybergenov, K., Alauadinov, A. (2017). 2-Local derivations on matrix algebras and algebras of measurable operators. Advances in Operator Theory, (), 17-28. doi: 10.22034/aot.1612-1074
Shavkat Ayupov; Karimbergen Kudaybergenov; Amir Alauadinov. "2-Local derivations on matrix algebras and algebras of measurable operators". Advances in Operator Theory, , , 2017, 17-28. doi: 10.22034/aot.1612-1074
Ayupov, S., Kudaybergenov, K., Alauadinov, A. (2017). '2-Local derivations on matrix algebras and algebras of measurable operators', Advances in Operator Theory, (), pp. 17-28. doi: 10.22034/aot.1612-1074
Ayupov, S., Kudaybergenov, K., Alauadinov, A. 2-Local derivations on matrix algebras and algebras of measurable operators. Advances in Operator Theory, 2017; (): 17-28. doi: 10.22034/aot.1612-1074
2-Local derivations on matrix algebras and algebras of measurable operators
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.