Lie Isomorphisms of Nest Algebras

In this paper we characterize linear mapsϕbetween two nest algebras T(N) and T(M) which satisfy the property thatϕ(AB−BA)=ϕ(A) ϕ(B)−ϕ(B) ϕ(A) for allA, B∈T(N). In particular, it is shown that such isomorphisms only exist if N is similar to M or M⊥.