@article {
author = {Ayupov, Shavkat and Kudaybergenov, Karimbergen and Alauadinov, Amir},
title = {2-Local derivations on matrix algebras and algebras of measurable operators},
journal = {Advances in Operator Theory},
volume = {2},
number = {4},
pages = {494-505},
year = {2017},
publisher = {Tusi Mathematical Research Group (TMRG)},
issn = {2538-225X},
eissn = {2538-225X},
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.},
keywords = {Matrix algebra,derivation,inner derivation,$2$-local derivation,measurable operator},
url = {http://www.aot-math.org/article_43482.html},
eprint = {http://www.aot-math.org/article_43482_5c7c7ad78c756b7cccec7aecf018feb2.pdf}
}