Perturbation of frames and Riesz bases in Hilbert C∗-modules

We extend the Casazza–Christensen general perturbation theorem for Hilbert space frames to modular frames in Hilbert C∗-modules. In the Hilbert space setting, under the same perturbation condition, the perturbation of any Riesz basis remains to be a Riesz basis. However, this result is no longer true for Riesz bases in Hilbert C∗-modules. We obtain a necessary and sufficient condition under which the perturbation (under Casazza–Christensen’s perturbation condition) of Riesz bases of Hilbert C∗-modules remains to be Riesz bases.