University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Controlled Continuous $G$-Frames and Their Multipliers in Hilbert Spaces37483496310.22130/scma.2019.68582.264ENYahyaAlizadehDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.Mohammad RezaAbdollahpourDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.Journal Article20170722In this paper, we introduce $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-frames is a $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(\mathcal{C},\mathcal{C}')$-controlled continuous $g$-Bessel multiplier is a p-Schatten class operator.https://scma.maragheh.ac.ir/article_34963_35384b34dcf883a65808ec86a7f3b34c.pdf