Iteration operator frames: duality and stability

The purpose of the paper is to analyze frames $\{f_k\}_{k \in \mathbb{Z}}$ having the form $\{T^{k}f_{0}\}_{k \in \mathbb{Z}}$; so called iteration operator frames for some bounded linear operator $T$ and a fixed vector $f_0$. We state the duality of such frames with respect to their generators. Moreover, we characterize all duals of iteration operator frames with the same structure. We also show that the duals of two iteration operator frames are close to each other provided that the original frames are sufficiently close to each other and vise versa.