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Additive derivations on generalized Arens algebras

  • S. Albeverio
  • Sh. A. Ayupov
  • R. Z. Abdullaev
  • K. K. Kudaybergenov
Article
  • 37 Downloads

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.

Keywords and phrases

von Neumann algebras measurable operator generalized Arens algebra additive derivation inner derivation 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • S. Albeverio
    • 1
    • 2
  • Sh. A. Ayupov
    • 3
    • 4
  • R. Z. Abdullaev
    • 3
  • K. K. Kudaybergenov
    • 5
  1. 1.Institut für Angewandte MathematikUniversitat BonnBonnGermany
  2. 2.SFB 611; HCM; BiBoS; IZKS; CERFIMLocarnoSwitzerland
  3. 3.Institute of Mathematics and Information TechnologiesUzbekistan Academy of SciencesTashkentUzbekistan
  4. 4.ICTPTriesteItaly
  5. 5.Karakalpak state universityNukusUzbekistan

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