A note on nonlinear skew Lie triple derivation between prime $\ast$-algebras
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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.
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.
참고문헌 (9)
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