In this paper, we investigate the mapping of continuous g-frames in Hilbert C*-module under bounded operators. So, operators that preserve continuous g-frames in Hilbert C*-module were characterized. Then, we introduce equivalent continuous g-frames in Hilbert C*-module by the mapping of continuous g-frames in Hilbert C*-module under bounded operators. We show that every continuous g-frame in H...

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.

The purpose of the paper is to analyze g-frames form \(\{\varphi T^{i} \in B(\mathcal {H},\mathcal {K})\}_{i=0}^\infty \), where \(T\in {H})\) and \(\varphi {K})\), discuss properties operator T. We consider stability g-Riesz sequences \). Finally, a weighted representation g frame introduced some its are presented. provide sufficient condition for given g-frame \(\Lambda =\{\Lambda _{i}\in {B(...

In this note we investigate the operators associated with frame sequences in a Hilbert space H, i.e., the synthesis operator T : l (N) → H , the analysis operator T ∗ : H → l (N) and the associated frame operator S = TT ∗ as operators defined on (or to) the whole space rather than on subspaces. Furthermore, the projection P onto the range of T , the projection Q onto the range of T ∗ and the Gr...

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

We introduce the notion of a g-atomic subspace for bounded linear operator and construct several useful resolutions identity on Hilbert space using theory g-fusion frames. Also we shall describe concept frame pair Bessel sequences some their properties.

This document contains supplementary materials for the paper Frames and numerical approximation by B. Adcock & D. Huybrechs [3]. SM1 Example 1. Fourier frames for complex geometries Consider the frame (3.1) over a domain Ω ⊆ (−1, 1)d. SM1.1 The kernel of G We first characterize the kernel of the Gram operator: Proposition SM1.1. Let G be the Gram operator (2.7) of the frame (3.1). Then Ker(G) =...

‎In this paper‎, ‎two iterative methods are constructed to solve the operator equation $ Lu=f $ where $L:Hrightarrow H $ is a bounded‎, ‎invertible and self-adjoint linear operator on a separable Hilbert space $ H $‎. ‎ By using the concept of frames of subspaces‎, ‎which is a generalization of frame theory‎, ‎we design some  algorithms based on Galerkin and Richardson methods‎, ‎and then we in...

Frames have turned out to be an essential tool for many applications such as, for example, data transmission, due to their robustness not only against noise but also against losses and due to their freedom in design [4, 6]. Their main advantage lies in the fact that a frame can be designed to be redundant while still providing a reconstruction formula. Since the frame operator Sg = ∑n i=1 〈g, f...