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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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참고문헌 (9)
참고문헌 신청
Z. Bai / 2012 / The structure of non-linear Lie derivations on factor von Neumann algebras / Linear Algebra Appl. 436:2701~2708
J. Cui / 2009 / Maps preserving product XY - Y X* on factor von Neumann algebras / Linear Algebra Appl. 431:833~842
C. Li / 2014 / Nonlinear $\xi$ -Jordan $\ast$ -derivations on von Neumann algebras / Linear and Multilinear Algebra. 62:466~473
C. Li / 2013 / Nonlinear mappings preserving product XY + Y X* on factor von Neumann algebras / Linear Algebra Appl. 438:2339~2345
C. LI / 2016 / Nonlinear Skew Lie Triple Derivations between Factors / Acta Mathematica Sinica 32:821~830
J. Cui / 2009 / Maps preserving product XY - Y X* on factor von Neumann algebras / Linear Algebra Appl. 431:833~842
C. Li / 2014 / Nonlinear
C. Li / 2013 / Nonlinear mappings preserving product XY + Y X* on factor von Neumann algebras / Linear Algebra Appl. 438:2339~2345
C. LI / 2016 / Nonlinear Skew Lie Triple Derivations between Factors / Acta Mathematica Sinica 32:821~830
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