Abstract:

Using methods of operator theory, the authors discussed P point *Lie derivation on factor von Neumann algebras. Let M be a factor von Neumann algebra acting on a complex Hilbert space H with dim H ≥2. We proved that if : M→M is a linear map satisfying (［A,B］*)=［(A),B］*+［A,(B)］* for all A,B∈M with AB=P, where P is a fixed nontrivial projection, then  is a *derivation.

Key words: von Neumann algebra, P point *Lie derivation, *derivation