a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion fram...

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+Ga...

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},mathca...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

In this paper, we investigate the mapping of continuous g-frames in Hilbert C*-module under bounded operators. So, operators that preserve continuous g-frames in Hilbert C*-module were characterized. Then, we introduce equivalent continuous g-frames in Hilbert C*-module by the mapping of continuous g-frames in Hilbert C*-module under bounded operators. We show that every continuous g-frame in H...