Additive derivations on generalized Arens algebras

Abstract

Given a von Neumann algebra $M$ with a faithful normal finite trace $\tau$ denote by $L^{\Lambda }(M,\tau )$ the generalized Arens algebra with respect to $M.$ We give a complete description of all additive derivations on the algebra $L^{\Lambda }(M,\tau ).$ In particular each additive derivation on the algebra $L^{\Lambda }(M,\tau ),$ where $M$ is a type II von Neumann algebra, is inner.

References in corpus (1)

• Additive derivations on algebras of measurable operators