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

Year 2024, , 595 - 607, 27.06.2024

Xiang Chun Xiao , Guo Ping Zhao , Guorong Zhou

https://doi.org/10.15672/hujms.1130102

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.

Keywords

K-g-frame, exact K-g-frame, weaving, Q-dual

Supporting Institution

Natural Science Foundation of Fujian Province, China; Xiamen University of Technology

Project Number

2020J01267 and 2021J011192; 40199071 and 50419004

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