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Let \({H}\) be a complex Hilbert space of dimension greater than \({3}\). We show that every surjective 2-local \({*}\)-Lie isomorphism \({\Phi}\) of \({B(H)}\) has the form \({\Phi=\Psi+\tau}\), where \({\Psi}\) is a \({*}\)-isomorphism or the negative of a \({*}\)-anti-isomorphism of \({B(H)}\), and \({\tau}\) is a homogeneous map from \({B(H)}\) into \({\mathbb{C}I}\) vanishing on every sum of commutators.  相似文献
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Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.  相似文献
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Let ℛ be a ring containing a nontrivial idempotent. In this article, under a mild condition on ℛ, we prove that if δ is a Lie triple derivable mapping from ℛ into ℛ, then there exists a Z A, B (depending on A and B) in its centre 𝒵(ℛ) such that δ(A + B) = δ(A) + δ(B) + Z A, B . In particular, let ℛ be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ℛ, if δ is a Lie triple derivable mapping from ℛ into ℛ, then δ = D + τ, where D is an additive derivation from ℛ into its central closure T and τ is a mapping from ℛ into its extended centroid 𝒞 such that τ(A + B) = τ(A) + τ(B) + Z A, B and τ([[A, B], C]) = 0 for all A, B, C ∈ ℛ.  相似文献
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本文证明了在没有中心交换投影的von Neumann代数上的一个双映射$\Phi$如果保持混合Jordan三重积, 则$\Phi(I)\Phi$是一个线性*-同构和一个共轭线性*-同构的和, 其中$\Phi(I)$是中心自伴元素且$\Phi(I)^{2}=I$. 同时给出了因子von Neumann 代数上保持混合Jordan三重积映射的结构.  相似文献
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