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Research articles

ScienceAsia 42(2016): 222-230 |doi: 10.2306/scienceasia1513-1874.2016.42.222

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.

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College of Mathematics and Computer Science, Shangrao Normal University, 401 Zhimin Street, Xinzhou District, Shangrao 334001, Jiangxi Province, China

* Corresponding author, E-mail: lxsy20110927@163.com

Received 27 Oct 2015, Accepted 0 0000