Additive derivations on generalized Arens algebras
Sergio AlbeverioInstitut für Angewandte Mathematik, Universitat Bonn, Endenicher Allee. 60, D-53115, Bonn, GermanySh. A. AyupovICTP, Trieste, ItalyR. Z. AbdullaevInstitute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Dormon Yoli str. 29, 100125, Tashkent, UzbekistanKarimbergen KudaybergenovKarakalpak state university, Ch Abdirov str. 1, 142012, Nukus, Uzbekistan
ABI
Abstract
Given a vonNeumann 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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