Geodesic
Derivations of Noncommutative Arens Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 70-72

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The present paper deals with derivations of noncommutative Arens algebras. We prove that every derivation of an Arens algebra associated with a von Neumann algebra and a faithful normal finite trace is inner. In particular, each derivation on such algebras is automatically continuous in the natural topology, and in the commutative case, even for semi-finite traces, all derivations are identically zero. At the same time, the existence of noninner derivations is proved for noncommutative Arens algebras with a semi-finite but nonfinite trace.
Keywords: von Neumann algebra, finite trace, Arens algebra, derivation, inner derivation. 
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     author = {Sh. A. Ayupov and K. K. Kudaibergenov},
     title = {Derivations of {Noncommutative} {Arens} {Algebras}},
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Sh. A. Ayupov; K. K. Kudaibergenov. Derivations of Noncommutative Arens Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 70-72. http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a5/