Local and 2-local Lie derivations of operator algebras on Banach spaces (Q395620)

Let \(B(X)\) be the algebra of bounded linear operators on a Banach space \(X\). The authors show that every local Lie derivation on \(B(X)\) is a Lie derivation and that every 2-local Lie derivation on \(B(X)\) has the form \(A\mapsto AT-TA+\psi(A)\), where \(T\in B(X)\) is a fixed operator and \(\psi:B(X)\to \mathbb FI\) is a homogeneous map satisfying \(\psi(A+B)=\psi(A)\) for \(A,B\in B(X)\) with \(B\) being a sum of commutators.