Additive mappings that preserve rank one nilpotent operators Original Research Article

Let B(X) be the algebra of bounded operators on a complex infinite dimensional Banach space X, and F(X) be the subalgebra of all finite rank operators in B(X). A characterization of additive mappings on F(X) which preserve rank one nilpotent operators in both directions is given. As applications of this result, some additive preservers are described.