Local derivations on measurable operators and commutativity

Abstract

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.

8 pages. arXiv admin note: text overlap with arXiv:1602.04959

References in corpus (2)

• Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras
• Spatiality of derivations on the algebra of $\tau$-compact operators