2010/04/10 by Qi, Xiaofei, Hou, Jinchuan
#16W25 #47L35 #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1004.1704
The additive (generalized) ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map L is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) ξ-Lie derivation with ξ\not=1 if and only if it is an additive (generalized) derivation satisfying L(ξA)=ξL(A) for all A. These results are then used to characterize additive (generalized) ξ-Lie derivations on several operator algebras such as Banach space standard operator algebras and von Neumman algebras.