University of MaraghehSahand Communications in Mathematical Analysis2322-580717120200101On Sum and Stability of Continuous $G$-Frames1571693734010.22130/scma.2018.90101.472ENAzamYousefzadeheyniDepartment of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.Mohammad RezaAbdollahpourDepartment of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.Journal Article20180717In 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.http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf