Additive derivations on generalized Arens algebras

Lobachevskii Journal of Mathematics 10/2010; 32(3). DOI: 10.1134/S1995080211030024
Source: arXiv


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.

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Available from: Sh. A. Ayupov