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 fra...

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...

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...

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 .

The g-frame operator for g-frame in Hilbert space is introduced. The results of g-frame operator are presented. A sequence of operators Λ̄j∈J(where Λ̄ = ΛSg −1 ) is a g-frame for the Hilbert space H with frame bounds 1 B and 1 A . Frame identities for g-normalized tight frames are established. Results on direct sum of gframe operators on direct sum of Hilbert spaces are presented. Mathematics Sub...

In this paper, we introduce the concept of dual frame of g-p-frame, and give the sufficient condition for a g-p-frame to have dual frames. Using operator theory and methods of functional analysis, we get some new properties of g-p-frame. In addition, we also characterize g-p-frame and g-q-Riesz bases by using analysis operator of g-p-Bessel sequence. c ©2017 All rights reserved.

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...