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arXiv · 1010.5117

Additive derivations on generalized Arens algebras

S. Albeverio·Sh. A. Ayupov·R. Z. Abdullaev·K. K. Kudaybergenov
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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.

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S. Albeverio, Sh. A. Ayupov, R. Z. Abdullaev, K. K. Kudaybergenov. 2010-10-25. Additive derivations on generalized Arens algebras. https://arxiv.org/abs/1010.5117

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