Abstract
Letℳbe any von Neumann algebra without central summands of typeI1andPa core-free projection with the central carrierI. For any scalarξ, it is shown that every additive mapLonℳsatisfiesL(AB-ξBA)=L(A)B-ξBL(A)+AL(B)-ξL(B)AwheneverAB=Pif and only if (1)ξ=1,L=φ+h, whereφis an additive derivation andhis a central valued additive map vanishing onAB-BAwithAB=P; (2)ξ≠1,Lis a derivation withL(ξA)=ξL(A)for eachA∈ℳ.
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