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On Sum and Stability of Continuous $G$-Frames

Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 1)

Publication Date:

Authors : ; ;

Page : 157-169

Keywords : Continuous $g$-frame; Parseval continuous $g$-frame; Continuous $g$-Bessel family; stability;

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Abstract

In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.

Last modified: 2020-06-16 17:02:43