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Additive Lie ($\xi$-Lie) derivations and generalized Lie ($\xi$-Lie) derivations on nest algebras. (English) Zbl 1207.47081
Summary: For a scalar $\xi$, a notion of (generalized) $\xi$-Lie derivations is introduced which coincides with the notion of (generalized) Lie derivations if $\xi =1$. Some characterizations of additive (generalized) $\xi$-Lie derivations on the triangular algebras and the standard operator subalgebras of Banach space nest algebras are given. 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) $\xi$-Lie derivation with $\xi \neq 1$ if and only if it is an additive (generalized) derivation satisfying $L(\xi A)=\xi L(A)$ for all $A$.

##### MSC:
 47L35 Nest algebras, CSL algebras 16W25 Derivations, actions of Lie algebras (associative rings and algebras)
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##### References:
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