Characterizations of Lie derivations of \(B(X)\)
The authors study a variant of the concept of a Lie derivation in the setting of bounded linear operators on a Banach space \(X\) of dimension at least~\(3\). The two results proven in this paper state that, if \(\delta: B(X)\to B(X)\) is a linear mapping satisfying the Lie derivation property on commutators \([a,b]\) with (i) \(ab=0\) or (ii) \(ab\) is a fixed non-trivial idempotent~\(p\), then \(\delta\) is the sum of a derivation \(d\) on \(B(X)\) and a linear centre-valued mapping \(\tau\) vanishing on commutators \([a,b]\) satisfying (i) or (ii), respectively.
scientific article; zbMATH DE number 5650021
scientific article