Nonlinear Lie-type derivations of von Neumann algebras and related topics

Tom 132 / 2013

Ajda Fošner, Feng Wei, Zhankui Xiao Colloquium Mathematicum 132 (2013), 53-71 MSC: 47B47, 46L57. DOI: 10.4064/cm132-1-5


Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let $\mathcal {A}$ be a von Neumann algebra without abelian central summands of type $I_1$. It is shown that every nonlinear Lie $n$-derivation of $\mathcal {A}$ has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each $(n-1)$th commutator of $\mathcal {A}$. Several potential research topics related to our work are also presented.


  • Ajda FošnerFaculty of Management
    University of Primorska
    Cankarjeva 5
    SI-6104 Koper, Slovenia
  • Feng WeiSchool of Mathematics
    Beijing Institute of Technology
    Beijing, 100081, P.R. China
  • Zhankui XiaoSchool of Mathematical Sciences
    Huaqiao University
    Quanzhou, Fujian, 362021, P.R. China

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