Local derivations on measurable operators and commutativity
  We prove that a von Neumann algebra $M$ is abelian if and only if the square of every derivation on the algebra $S(M)$ of measurable operators, affiliated with $M$, is a local derivation. We also show that for general associative unital algebras this is not true. 
Shavkat Ayupov and Karimbergen Kudaybergenov
math.OA