ScienceAsia 42(2016): 222-230 |doi:
Frame sequences and dual frames for operators
Zhong-Qi Xiang*, Yong-Ming Li
ABSTRACT: We introduce the more general frame sequences and dual frames related to a linear bounded operator K in Hilbert spaces which we call K-frame sequences and dual K-frames, respectively. We give several equivalent characterizations for K-frame sequences. We also investigate the relationships among K-frame sequences, K-frames, and frame sequences, and give a new perturbation result for K-frames by using the associated dual K-frames. It turns out that in many ways K-frame sequences and dual K-frames behave completely differently from frame sequences and dual frames, respectively.
|College of Mathematics and Computer Science, Shangrao Normal University, 401 Zhimin Street, Xinzhou District, Shangrao 334001, Jiangxi Province, China
* Corresponding author, E-mail: email@example.com
Received 27 Oct 2015, Accepted 7 Jun 2016