Additive mappings that preserve rank one nilpotent operators.
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 maps on \(F(X)\) which preserve rank one nilpotent operators in both directions is given. As application of this result, some additive preservers are obtained.
scientific article; zbMATH DE number 1917813