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...

Abstract As generalizations of g-frames and controlled frames, the theory has been deeply studied. This paper addresses dual in Hilbert spaces. We first present some equivalent characterizations g-frames. Then, we introduce concepts operator, get properties them. Finally, obtain for a given g-frame by method operator theory.

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

In this paper we introduce controlled *-g-frame and *-g-multipliers in Hilbert C*-modules and investigate the properties. We demonstrate that any controlled *-g-frame is equivalent to a *-g-frame and define multipliers for (C,C')- controlled*-g-frames .

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...