Additive Lie (xi-Lie) derivations and generalized Lie (xi-Lie) derivations on nest algebras

摘要

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 not equal 1 if and only if it is an additive (generalized) derivation satisfying L(xi A) = xi L(A) for all A. (C) 2009 Elsevier Inc. All rights reserved.