Finite extensions of Bessel sequences

Abstract

The paper studies finite extensions of Bessel sequences in infinite-dimensional Hilbert spaces. We provide a characterization of Bessel sequences that can be extended to frames by adding finitely many vectors. We also characterize frames that can be converted to Parseval frames by finite-dimensional perturbations. Finally, some results on excesses of frames and near-Riesz bases are derived.

13 pages

Cited by in corpus (3)

• On excesses of frames
• Expansion of approximate Bessel sequences to approximate Schauder frames for Banach spaces
• Expansions from frame coefficients with erasures