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Related papers: A note on perturbations of Fusion Frames

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Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…

Controlled g-atomic subspace for a bounded linear operator is being presented and a characterization has been given. We give an example of controlled K-g-fusion frame. We construct a new controlled K-g-fusion frame for the Hilbert space H ?…

Functional Analysis · Mathematics 2023-03-29 Prasenjit Ghosh , T. K. Samanta

Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…

Mathematical Physics · Physics 2012-10-12 J-P. Antoine , P. Balazs

Frame theory is recently an active research area in mathematics, computer science, and engineering with many exciting applications in a variety of different fields. In this paper, we firstly give a characterization of operator frame for…

Functional Analysis · Mathematics 2019-05-06 Mohamed Rossafi , Abdellatif Akhlidj

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special…

Functional Analysis · Mathematics 2018-06-12 Vahid Sadri , Reza Ahmadi , Asghar Rahimi

One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…

Functional Analysis · Mathematics 2024-04-26 Salah Eddine Oustani , Mohamed Rossafi

Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their…

General Mathematics · Mathematics 2025-06-17 Prasenjit Ghosh , Jayanta Ghosh , T. K. Samanta

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…

Functional Analysis · Mathematics 2015-02-20 Jaydeb Sarkar

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…

Functional Analysis · Mathematics 2018-06-12 Vahid Sadri , Gholamreza Rahimlou , Reza Ahmadi , Ramazan Zarghami

The purpose of the paper is to analyze frames $\{f_k\}_{k\in \mathbf Z}$ having the form $\{T^kf_0\}_{k\in\mathbf Z}$ for some linear operator $T: \mbox{span} \{f_k\}_{k\in \mathbf Z} \to \mbox{span}\{f_k\}_{k\in \mathbf Z}$. A key result…

Functional Analysis · Mathematics 2017-05-01 Ole Christensen , Marzieh Hasannasab

The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…

Functional Analysis · Mathematics 2022-12-15 Roumaissae Eljazzar , Mohamed Rossafi , Choonkil Park

Motivated by the study of frame properties arising from iterates of linear operators, it was previously established that the multiplication operator $T_{\phi}x(t) = \phi(t)x(t)$ cannot generate a frame in $L^2(a,b)$ (Results Math, 2019). In…

Functional Analysis · Mathematics 2025-09-08 Jahangir Cheshmavar

In this paper we introduced the concept of continuous relay fusion frames in Hilbert spaces. And we define the dual frames for continuous relay fusion frames. Finally we study the perturbation probleme of continuous relay fusion frames.

Functional Analysis · Mathematics 2023-01-02 Fakhr-dine Nhari , Mohamed Rossafi

For an invertible linear operator $T$ on a Hilbert space $H$, put \[ \alpha(T^*,T) := -T^{*2}T^2 + (1+r^2) T^* T - r^2 I, \] where $I$ stands for the identity operator on $H$ and $r\in (0,1)$; this expression comes from applying Agler's…

Functional Analysis · Mathematics 2021-09-09 Glenier Bello , Dmitry Yakubovich

A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down…

Functional Analysis · Mathematics 2007-05-23 Peter G. Casazza , Ole Christensen

Let $T$ and $V$ be two Hilbert space contractions and let $X$ be a linear bounded operator. It was proved by C. Foias and J.P. Williams that in certain cases the operator block matrix $R(X;T,V)$ (defined in the text) is similar to a…

Functional Analysis · Mathematics 2007-05-23 Catalin Badea

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

Functional Analysis · Mathematics 2014-06-30 M. Mantoiu , D. Parra

We investigate the structured frames for Hilbert $C^{*}$-modules. In the case that the underlying $C^{*}$-algebra is a commutative $W^*$-algebra, we prove that the set of the Parseval frame generators for a unitary operator group can be…

Functional Analysis · Mathematics 2007-05-23 Wu Jing , Deguang Han , Ram Mohapatra

For applications like the numerical solution of physical equations a discretization scheme for operators is necessary. Recently frames have been used for such an operator representation. In this paper, we apply fusion frames for this task.…

Functional Analysis · Mathematics 2019-10-31 Mitra Shamsabadi , Ali Akbar Arefijamaal , Peter Balazs

Recent research has shown that the properties of overcomplete Gabor frames and frames arising from shift-invariant systems form a precise match with certain conditions that are necessary for a frame in $L^2(\mathbf R)$ to have a…

Functional Analysis · Mathematics 2017-05-02 Ole Christensen , Marzieh Hasannasab