Document Type : Research Paper

**Authors**

Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.

**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 p-Schatten class operator.

**Keywords**

- Controlled continuous $g$-frames
- $(mathcal{C}
- mathcal{C}')$-controlled continuous $g$-Bessel families
- Multiplier of continuous $g$-frames

**Main Subjects**

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