Nonlinear maps preserving similarity on image Original Research Article

Let X be a real or complex Banach space with dimension at least 3, image be the family of all rank one nilpotent operators. We give the concrete form of every bijective map image such that image. Based on this result, we characterize the surjective map image for all image, where H is a Hilbert space (real or complex) with dimension at least 3.