In this talk we present several results regarding frame perturbations which we will state as equivalent results for perturbations of their respective analysis/synthesis operators. We will give a characterization of frames that have a sufficiently close Parseval frame, i.e., lower bounded operators that have a sufficiently close isometry. Also, we will derive some bounds on the distance of dual frames and show that pseudo-dual frames have the same excess. From this fact we get as an easy consequence that close enough perturbations of frames have the same excess - an already known result which we prove in a much simpler way. All the results will be presented in an operator theory setting.
This is a joint work with Damir Bakić.