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...

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator SW , which in turn is heavily dependent on the sparsity of SW . We will show that sparsity of ...

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...

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.

In this paper, we study frames for bounded linear operators and defined the notion of Ad-operator frame for Banach spaces. A necessary and sufficient condition for a sequence of bounded linear operators to be an Ad-operator frame has been given. Some characterizations of Ad-operator frames have been discussed. Further, a method has been given to generate a -Banach frame using a Schauder frame. ...

In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...

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...

Abstract. The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with particular properties and motivates our results. We find a necessary and sufficient condition under which any positive finite-rank operator B can be e...

Let H be a separable Hilbert space, let G ⊂ H, and let A be an operator on H. Under appropriate conditions on A andG, it is known that the set of iterations FG(A) = {Ag | g ∈ G, 0 ≤ j ≤ L(g)} is a frame for H. We call FG(A) a dynamical frame for H, and explore further its properties; in particular, we show that the canonical dual frame of FG(A) also has an iterative set structure. We explore th...