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. Published by Elsevier Inc.