Local and 2-Local derivations on noncommutative Arens algebras

Abstract

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra $L^{\omega }(M,\tau )$ associated with a von Neumann algebra $M$ and a faithful normal semi-finite trace $\tau .$ We prove that every 2-local derivation on $L^{\omega }(M,\tau )$ is a spatial derivation, and if $M$ is a finite von Neumann algebra, then each local derivation on $L^{\omega }(M,\tau )$ is also a spatial derivation and every 2-local derivation on $M$ is in fact an inner derivation.

13 pages

Cited by in corpus (2)

• 2-local derivations on semi-finite von Neumann algebras
• 2-Local derivations and automorphisms on $B(H)$