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

Authors : Xiang Chun Xiao, Guo Ping Zhao, Guorong Zhou

Pages : 595-607

Doi:10.15672/hujms.1130102

View : 103 | Download : 220

Publication Date : 2024-06-27

Article Type : Research Paper

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