Abstract
In this paper, we introduce the more general g-frame which is called a $K$-g-frame by combining a g-frame with a bounded linear operator $K$ in a Hilbert space. We give several equivalent characterizations for $K$-g-frames and discuss the stability of perturbation for $K$-g-frames. We also investigate the relationship between a $K$-g-frame and the range of the bounded linear operator $K$. In the end, we give two sufficient conditions for the remainder of a $K$-g-frame after an erasure to still be a $K$-g-frame. It turns out that although $K$-g-frames share some properties similar to g-frames, a large part of $K$-g-frames behaves completely different from g-frames.
Citation
Xiang-chun Xiao. Yu-can Zhu. Zhi-biao Shu. Ming-ling Ding. "G-frames with bounded linear operators." Rocky Mountain J. Math. 45 (2) 675 - 693, 2015. https://doi.org/10.1216/RMJ-2015-45-2-675
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