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.
"Finite extensions of Bessel sequences." Banach J. Math. Anal. 9 (4) 1 - 13, 2015. https://doi.org/10.15352/bjma/09-4-1