Certain facts about frames and generalized frames are extended for the new g-frames, referred as *-g-frames, in a Hilbert C*-modules. As a matter of fact, some relations are establish between *-frames and *-g-frames in a Hilbert C*-module. Furthermore, the paper studies the operators associated to a given *-g-frame, the construction of new *-g-frames. Moreover, the operator duals for a *-g-frame are introduced and their properties are investigated. Finally, operator duals of a *-g-frame are characterized.

Fusion frames or frames of subspaces are an extension of frames that have many applications in science. The paper presents non-orthogonal fusion frames with real valued bounds and [Formula: see text]-valued bounds in Hilbert [Formula: see text]-modules which they are called NOFF and NO[Formula: see text]FF, respectively. Their elementary properties are studied, for example, the relations between NOFF and NO[Formula: see text]FF in Hilbert [Formula: see text]-modules are established. More precisely, we investigate these fusion frames in Hilbert [Formula: see text]-modules over different [Formula: see text]-algebras.

Theory of frames has very applications to various areas of science and engineering. The paper presents all duals of a constructed frame that is obtained by an operator and a primary frame. By two frames and their frame operators, a frame is given that has an identify frame operator. Moreover, a relation between ordinary duals and operator duals is given. Finally, an equation is introduced for pre-frame operator of a given frame and pre-frame operator of its operator dual.

The finite frame theory is a very important part offrame theory due to its significant relevance in various branchesof mathematical applications. Studying controlled inite frames isthe goal of the work. To this end, we introduce controlled framesin a inite-dimensional Hilbert space and study some properties ofthem. The main class of inite frames in frame applied problemsis Parseval frames. By viewpoint to this, a brief discussion aboutParseval frames is presented and also Parseval controlled framesare investigated. Afterward, the paper characterizes all operatorsthat construct controlled inite frames. Furthermore, controlledinite frames are also considered as a proper subset of dual framesby the equivalency relation between frames.