Abstract: Let H be a Hilbert space over the real or complex field F, N be a non-trivial nest on H and τ(N) be the associated nest algebra. Suppose s: τ(N)→τ(N) is a map without additivity and linearity. With the help of method of algebratic decomposition, we prove that if 3s(X^.Y^.Z)=s(X)^.Y^.Z+X^.s(Y)^. Z+X^.Y^.sZ) for any X,Y,Z∈τ(N ) with XYZ=0, then s is an additive centralizer.

Key words: nest algebra, nonlinear map, centralizer