The authors study a variant of the concept of a Lie derivation in the setting of bounded linear operators on a Banach space
of dimension at least 3. The two results proven in this paper state that, if
is a linear mapping satisfying the Lie derivation property on commutators
is a fixed non-trivial idempotent
is the sum of a derivation
and a linear centre-valued mapping
vanishing on commutators
satisfying (i) or (ii), respectively.