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On Weaving g-Frames for Hilbert Spaces

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Abstract

Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two necessary conditions in terms of frame bounds for weaving g-frames. Then we study the properties of weakly woven g-frames and give a sufficient condition for weaving g-frames. It is shown that weakly woven is equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz bases is considered. Finally, we present Paley–Wiener-type perturbation results for weaving g-frames.

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Acknowledgements

The research is supported by the the Natural Science Foundation of Anhui Province (No. 1908085MF175) and Fundamental Research Funds for the Central Universities (No. JZ2019HGBZ0129) and National Natural Science Foundation of China (Nos. 11271001 and 61370147), and the Fundamental Research Funds for the Central Universities (No. ZYGX2016KYQD143).

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Dongwei Li

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Jinsong Leng, Tingzhu Huang & Xiaoping Li

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  1. Dongwei Li
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  2. Jinsong Leng
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  3. Tingzhu Huang
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  4. Xiaoping Li
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Correspondence to Dongwei Li.

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Communicated by Ilwoo Cho.

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Li, D., Leng, J., Huang, T. et al. On Weaving g-Frames for Hilbert Spaces. Complex Anal. Oper. Theory 14, 33 (2020). https://doi.org/10.1007/s11785-020-00991-7

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