Related papers: Representations of $g$-fusion frames in Hilbert $C…
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
We give a characterization of K-g-fusion frames and discuss the stability of dual g-fusion frames. We also present a necessary and sufficient condition for a quotient operator to be bounded.
In this paper, we introduce controlled frames in Hilbert $C^*$-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert…
The purpose of this paper is to study frames for a Hilbert space ${\cal H},$ having the form $\{T^n \varphi\}_{n=0}^\infty$ for some $\varphi \in {\cal H}$ and an operator $T: {\cal H} \to {\cal H}.$ We characterize the frames that have…
In this Work, We introduce the concept of $\ast$-operator frame, which is a generalization of $\ast$-frames in Hilbert pro-$C^{\ast}$-modules, and we establish some results, we also study the tensor product of $\ast$-operator frame for…
To improve the numerical efficiency of iterative algorithms for inverting the frame operator, the controlled frame was introduced by Balazs et al. \cite{Balazs}, and has since been given more importance. In this paper, we introduce the…
In this paper, we introduce and study frame of operators in quaternionic Hilbert spaces as a generalization of g frames which in turn generalized various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion…
We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…
K-frames, a new generalization of frames, were recently considered by L. Gavruta in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a…
After introducing g-frames and fusion frames by Sun and Casazza, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give…
Motivated by recent work in Dynamical Sampling, we prove a necessary and sufficient condition for a frame in a separable and infinite-dimensional Hilbert space to admit the form $\{T^{n} \varphi \}_{n \geq 0}$ with $T \in B(H)$. Also, a…
We present the notion of continuous controlled K-g-fusion frame in Hilbert space which is the generalization of discrete controlled K-g-fusion frame. We discuss some characterizations of continuous controlled K-g-fusion frame. Relationship…
Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n \varphi\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…
It is known that it is a very restrictive condition for a frame $\{f_k\}_{k=1}^\infty$ to have a representation $ \{T^n \varphi\}_{n=0}^\infty$ as the orbit of a bounded operator $T$ under a single generator $\varphi\in\mathcal{H}.$ In this…
An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…
Dynamical sampling deals with representations of a frame $\{ f_k \}_{k=1}^\infty$ as an orbit $\{ T^n \varphi \}_{n=0}^\infty$ of a linear and possibly bounded operator $T$ acting on the underlying Hilbert space. It is known that the desire…
A bounded linear operator $T$ on a Hilbert space is said to be homogeneous if $\varphi(T)$ is unitarily equivalent to $T$ for all $\varphi$ in the group M\"{o}b of bi-holomorphic automorphisms of the unit disc. A projective unitary…
Dynamical sampling deals with frames of the form $\{T^n\varphi\}_{n=0}^\infty$, where $T \in B(\mathcal{H})$ belongs to certain classes of linear operators and $\varphi\in\mathcal{H}$. The purpose of this paper is to investigate a new…