Perturbations of frames
In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic. © 2014 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.
Acta Mathematica Sinica, English Series
Chen, D., Li, L., & Zheng, B. (2014). Perturbations of frames. Acta Mathematica Sinica, English Series, 30 (7), 1089-1108. https://doi.org/10.1007/s10114-014-2804-5