Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A NOTE ON NONLINEAR SKEW LIE TRIPLE DERIVATION BETWEEN PRIME ⁎-ALGEBRAS

  • Taghavi, Ali (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran) ;
  • Nouri, Mojtaba (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran) ;
  • Darvish, Vahid (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
  • Received : 2018.05.06
  • Accepted : 2018.07.17
  • Published : 2018.09.30
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Abstract

Recently, Li et al proved that ${\Phi}$ which satisfies the following condition on factor von Neumann algebras $${\Phi}([[A,B]_*,C]_*)=[[{\Phi}(A),B]_*,C]_*+[[A,{\Phi}(B)]_*,C]_*+[[A,B]_*,{\Phi}(C)]_*$$ where $[A,B]_*=AB-BA^*$ for all $A,B{\in}{\mathcal{A}}$, is additive ${\ast}-derivation$. In this short note we show the additivity of ${\Phi}$ which satisfies the above condition on prime ${\ast}-algebras$.

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References

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