2-local Lie derivations of nest subalgebras of factors

Let beta be a non-trivial nest in an arbitrary factor M. We prove that every additive 2-local Lie derivation delta from nest subalgebra alg(M)beta into M can be written in the form delta(A) = AT - TA + h(A) I for all A is an element of alg(M)beta, where T is an element in M and h is a linear functional vanishing on each commutator. We also provide an example to show the additivity of d is necessary.