Von Neumann代数上P点ξ-Lie导子的刻画

Characterization of ξ-Lie Derivations at P Point on Von Neumann Algebras

设A是没有I_1型中心直和项的von Neumann代数,P∈A是一个非中心的空核投影且其中心包络是I.研究了Von Neumann代数上P点ξ-Lie导子δ,得到了对任意A∈A,存在T∈A使得δ(A)=AT-TA,这里非零数ξ∈F且ξ≠±1.

Let A be a von Neumann algebra without central summands of type I_1,and P ∈ A is a non-central core-free projection with central carrier I.We study ξ-Lie derivationδ at P point on A,and obtain there exists a.T ∈ A such that δ（A） = AT- TA for all A ∈ A,where ξ ∈ F is a non-zero scalar with ξ≠ ±1.