Abstract :
In 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 pSchatten class operator.
