On excesses of frames

Abstract

We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. We then prove that pseudo-dual frames and, in particular, approximately dual frames have the same excess. We also discuss various results on frames in which excesses of frames play an important role.

12 pages

References in corpus (2)

• Finite extensions of Bessel sequences
• Approximately dual frame pairs in Hilbert spaces and applications to Gabor frames

Cited by in corpus (5)

• Some perturbation results for quasi-bases and other sequences of vectors
• The effect of perturbations of frames on their alternate and approximately dual frames
• Approximately Dual and Pseudo-Dual Probabilistic Frames
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• Expansions from frame coefficients with erasures