因子von Neumann代数上非线性*-Lie导子的刻画

Characterization of Nonlinear *-Lie Derivations on Factor von Neumann Algebras

设M是Hilbert空间H上维数大于1的因子von Neumann代数,给出M上非线性*-Lie三重导子的定义,并用代数Pierce分解方法证明:如果Φ:M→M是一个非线性*-Lie三重导子,则Φ是非线性*-Lie导子.

Let M be a factor von Neumann algebra on a Hilbert space H in which the dimension of M is larger than one. We give the definition of nonlinear *-Lie triple derivation on M. By the method of Pierce decomposition, it is proved that if Φ: M→M is a nonlinear *-Lie triple derivation, Φ is a nonlinear *-Lie derivation.