Bilocal Lie derivations on nest algebras

Abstract

Let be a nest on a complex separable Hilbert space H and be the associated nest algebra. In this paper, we prove that every bilocal Lie derivation from into itself is of the form , where , and is a linear map vanishing on each commutator. Moreover, we show that every bilocal Lie derivation from into itself is a Lie derivation if is a non-atomic nest or there exists an atom E of with .