In this paper, a new notion of frames is introduced: $ast$-operator frame as generalization of $ast$-frames in Hilbert $C^{ast}$-modules introduced by A. Alijani and M. A. Dehghan cite{Ali} and we establish some results.

‎Frames generalize orthonormal bases and allow representation of all the elements of the space‎. ‎Frames play significant role in signal and image processing‎, ‎which leads to many applications in informatics‎, ‎engineering‎, ‎medicine‎, ‎and probability‎. ‎In this paper‎, ‎we introduce the concepts of operator frame for the space $End_{mathcal{A}}^{ast}(mathcal{H})$ of all adjointable operator...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.