TY  - JOUR
T1  - Redundancy, weaving and $Q$-dual of $K$-g-frames in Hilbert spaces
AU  - Xiao, Xiang Chun
AU  - Zhao, Guo Ping
AU  - Zhou, Guorong
PY  - 2024
DA  - June
DO  - 10.15672/hujms.1130102
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 595
EP  - 607
VL  - 53
IS  - 3
LA  - en
AB  - 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.
KW  - K-g-frame
KW  - exact K-g-frame
KW  - weaving
KW  - Q-dual
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UR  - https://doi.org/10.15672/hujms.1130102
L1  - https://dergipark.org.tr/en/download/article-file/2483763
ER  -