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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 53 Issue: 3

Redundancy, weaving and $Q$-dual of $K$-g-frames in Hilbert spaces

Xiang Chun Xiao(Xiamen University of Technology)0000-0002-0030-2688
Guo Ping Zhao(Xiamen University of Technology)0000-0002-1832-9264
Guorong Zhou(Xiamen University of Technology)0000-0002-8063-5043
Pages
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Publication Date
2024-06-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we characterize the $Q$-dual of g-frames using their induced sequences.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study exact $K$-g-frames, weaving of $K$-g-frames and $Q$-duals of g-frames in Hilbert spaces.
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Key Findings & Data:We present a sufficient condition for a g-Bessel sequence to be an exact $K$-g-frame.
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Conclusion & Impact:Finally, we characterize the $Q$-dual of g-frames using their induced sequences.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:K-g-frame · exact K-g-frame · weaving

Abstract

In this paper we study exact $K$-g-frames, weaving of $K$-g-frames and $Q$-duals of g-frames in Hilbert spaces. We present a sufficient condition for a g-Bessel sequence to be an exact $K$-g-frame. Given two woven pairs $(\Lambda, \Gamma)$ and $(\Theta, \Delta)$ of $K$-g-frames, we investigate under what conditions $\Lambda$ can be $K$-g-woven with $\Delta$ if $\Gamma$ is $K$-g-woven with $\Theta$. Given a $K$-g-frame $\Lambda$ and its dual $\Gamma$ on $\mathcal{U}$, we construct a new pair based on $\Lambda$ and $\Gamma$ so that they are woven on a subspace $R(K)$ of $\mathcal{U}$. Finally, we characterize the $Q$-dual of g-frames using their induced sequences.

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Cite This Article

Xiao, X. C., Zhao, G. P., Zhou, G. (2024). Redundancy, weaving and $Q$-dual of $K$-g-frames in Hilbert spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 3. https://doi.org/10.15672/hujms.1130102

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