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Related papers: Some generalizations of frames in Hilbert modules

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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…

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson

Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…

Functional Analysis · Mathematics 2021-12-10 Yuxiang Xu , Dongwei Li , Jinsong Leng

In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…

Functional Analysis · Mathematics 2009-02-12 Peter Balazs

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…

Functional Analysis · Mathematics 2017-05-02 Fahimeh Arabyani Neyshaburi , Ali Akbar Arefijamaal

Frame Theory has a great revolution for recent years. This Theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. The purpose of this paper is the introduction and the study of the new concept that of Continuous…

Functional Analysis · Mathematics 2020-07-08 Abdeslam Touri , Hatim Labrigui , Samir Kabbaj

In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.

Operator Algebras · Mathematics 2019-01-15 H. Labrigui , A. Touri , S. Kabbaj

In this paper we introduce the concepts of atomic systems for operators and K-frames in Hilbert C*-modules and we establish some results.

Operator Algebras · Mathematics 2014-03-04 Abbas Najati , M. Mohammadi Saem , P. Gavruta

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

Mathematical Physics · Physics 2017-02-23 M. Khokulan , K. Thirulogasanthar , S. Srisatkunarajah

The notion of controlled frames for Hilbert spaces were introduced by Balazs, Antoine and Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Controlled Frame Theory has a great revolution in…

Functional Analysis · Mathematics 2020-08-20 Hatim Labrigui , Samir Kabbaj

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

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

Mathematical Physics · Physics 2010-04-22 Nicolae Cotfas , Jean Pierre Gazeau

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

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…

Functional Analysis · Mathematics 2007-05-23 Wenchang Sun

Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi…

Functional Analysis · Mathematics 2025-08-26 Ole Christensen , Navneet Redhu , Niraj K. Shukla

This study aims at combining the concepts of $g$-frame and $K$-frame for a Hilbert $C^*$-module $U$, for an operator $K \in End^*_A(U)$, where $End^*_A(U)$ contains all adjointable $A$-linear maps on $U$. As a result, continuous…

Functional Analysis · Mathematics 2024-10-07 Jahangir Cheshmavar , Javad Baradaran , Asadollah Hossienpour

The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the…

Operator Algebras · Mathematics 2015-07-16 Ljiljana Arambašić , Damir Bakić

In this paper, we will introduce the concept of biframes for Hilbert $ C^{\ast}- $modules produced by a pair of sequences, and we present various examples of biframes. Then, we examine the characteristics of biframes from the viewpoint of…

Functional Analysis · Mathematics 2025-01-28 Mohamed Rossafi , Abdelilah Karara , Roumaissae El jazzar

This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…

Functional Analysis · Mathematics 2011-11-08 Bill Moran , Stephen Howard , Doug Cochran

In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…

Functional Analysis · Mathematics 2015-03-19 Abolhassan Fereydooni , Ahmad Safapour