On excesses of frames (Q2786996)

The paper is concerned with excesses of frames. In Theorem 2.2, the authors prove that dual frames have the same excess. This leads to some relations for the analysis, resp. synthesis operators of dual frames (see Corollaries 2.3 and 2.4). With Corollary 2.7, they prove that also pseudo-dual and approximately dual frames have the same excess. In addition, the authors include some results on frame perturbations, Parseval duals and the fundamental identity for Parseval frames, related to excesses of frames.