Additive derivations on generalized Arens algebras

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

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