2-Local {*}-Lie isomorphisms of operator algebras

Let \({H}\) be a complex Hilbert space of dimension greater than \({3}\). We show that every surjective 2-local \({*}\)-Lie isomorphism \({\Phi}\) of \({B(H)}\) has the form \({\Phi=\Psi+\tau}\), where \({\Psi}\) is a \({*}\)-isomorphism or the negative of a \({*}\)-anti-isomorphism of \({B(H)}\), and \({\tau}\) is a homogeneous map from \({B(H)}\) into \({\mathbb{C}I}\) vanishing on every sum of commutators.