Lie triple derivations on nest algebras

Abstract

Abstract Let δ be a Lie triple derivation from a nest algebra 𝒜 into an 𝒜‐bimodule ℳ︁. We show that if ℳ︁ is a weak* closed operator algebra containing 𝒜 then there are an element S ∈ ℳ︁ and a linear functional f on 𝒜 such that δ ( A ) = SA – AS + f ( A ) I for all A ∈ 𝒜, and if ℳ︁ is the ideal of all compact operators then there is a compact operator K such that δ ( A ) = KA – AK for all A ∈ 𝒜. As applications, Lie derivations and Jordan derivations on nest algebras are characterized. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)