因子von Neumann代数上的非线性混合ξ-Jordan三重可导映射

Nonlinear Mixedξ-Jordan Triple Derivable Maps on Factor von Neumann Algebras

设■是一个的因子von Neumann代数.我们证明了每一个非线性混合ξ-Jordan(ξ≠0,-1)三重可导映射Φ:■→■都是可加的*-导子,且对任意的A∈■,有Φ(ξA)=ξΦ(A).

Let ■ be a factor von Neumann algebra.We prove that each nonlinear mixed ξ-Jordan triple derivable map Φ:■→■ is an additive *-derivation andΦ(ξA)=ξΦ(A) for all A ∈■ with ξ≠0,-1.