Riesz bases and their dual modular frames in Hilbert C ∗-modules

We investigate dual frames of modular frames and Riesz bases in Hilbert C ∗-modules. In Hilbert C ∗-modules, a Riesz basis may have many dual modular frames, and it may even admit two different dual modular frames both of which are Riesz bases. We characterize those Riesz bases that have unique duals. In addition, we obtain a necessary and sufficient condition for a dual of a Riesz basis to be again a Riesz basis, and prove some new related results. © 2008 Published by Elsevier Inc.