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BY-NC-ND 3.0 license Open Access Published by De Gruyter May 8, 2014

Local and 2-local derivations on noncommutative Arens algebras

  • Shavkat Ayupov EMAIL logo , Karimbergen Kudaybergenov , Berdakh Nurjanov and Amir Alauadinov
From the journal Mathematica Slovaca

Abstract

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra L ω(M,τ) associated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every 2-local derivation on L ω(M,τ) is a spatial derivation, and if M is a finite von Neumann algebra, then each local derivation on L ω(M,τ) is also a spatial derivation and every 2-local derivation on M is in fact an inner derivation.

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Published Online: 2014-5-8
Published in Print: 2014-4-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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