Additive derivations on generalized Arens algebras

Details Additive derivations on generalized Arens algebras Additive derivations on generalized Arens algebras

2010-10-25

arxiv.org/abs/1010.5117v1

Mathematics

Operator Algebras

Scientific paper

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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