Abstract
In this paper we use two kinds of induced sequences of two g-frames \(\{\Lambda _j:j\in J\}\) and \(\{\Gamma _j:j\in J\}\) on \({\mathcal {U}}\) to characterize when \(\{\Lambda _j:j\in J\}\) and \(\{\Gamma _j:j\in J\}\) are woven on \({\mathcal {U}}\), and vice versa. Meanwhile, we present an example to show that a result obtained by Deepshikha et al. on an equivalent characterization of two K-g-frames being woven on \({\mathcal {U}}\) is incorrect.
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No data, models, or code were generated or used during the study.
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Acknowledgements
We thank the anonymous referees for valuable suggestions and comments, which lead to a significant improvement of our manuscript. This work is partly supported by the Natural Science Foundation of Fujian Province, China (Grant Nos. 2020J01267 and 2021J011192), and the projects of Xiamen University of Technology (Grant Nos. 40199071 and 50419004).
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Xiao, X., Zhao, G. & Zhou, G. Characterizations of weaving for g-frames by induced sequences. J. Pseudo-Differ. Oper. Appl. 12, 60 (2021). https://doi.org/10.1007/s11868-021-00430-x
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DOI: https://doi.org/10.1007/s11868-021-00430-x