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Related papers: Frames and operators in Hilbert C*-modules

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The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital…

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

K-frames were recently introduced by L. G\v{a}vruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by P. Balazs in Hilbert spaces to improve the…

Functional Analysis · Mathematics 2016-02-15 Asghar Rahimi , Shahram Najafzadeh , Mohamad Nouri

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

Frame Theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper, we introduce the concept of Controlled K-operator frame for the space…

Functional Analysis · Mathematics 2020-08-14 Abdeslam Touri , Samir Kabbaj

The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also,…

Functional Analysis · Mathematics 2022-12-06 Jahangir Cheshmavar , Ayyaneh Dallaki

In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g…

Functional Analysis · Mathematics 2019-05-15 E. Alizadeh , M. H. Faroughi , M. Rahmani

Our main goal in this paper, is to generalize to Hilbert C*-modules the concept of fusion frames. Indeed we introduce the notion of *\~nfusion frames associated to weighted sequences of orthogonally complemented submodules of a Hilbert…

General Mathematics · Mathematics 2023-08-22 Nadia Assila , Samir Kabbaj , Hicham Zoubeir

This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a…

Operator Algebras · Mathematics 2024-05-30 Roumaissae Eljazzar , Mohammed Mouniane , Mohamed Rossafi

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…

Functional Analysis · Mathematics 2019-04-15 N. K. Sahu

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

Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator…

Operator Algebras · Mathematics 2007-09-26 Victor Kaftal , David Larson , Shuang Zhang

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

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…

Mathematical Physics · Physics 2007-05-23 N. P. Landsman

Frame Theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper, we introduce the concept of Controlled $\ast$-$K$-operator frame for the space…

Functional Analysis · Mathematics 2023-02-16 Hatim Labrigui , Mohamed Rossafi , Abdeslam Touri , Nadia Assila

In this paper, we will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames…

Functional Analysis · Mathematics 2024-03-12 Abdelilah Karara , Mohamed Rossafi

In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by…

Functional Analysis · Mathematics 2024-02-27 Abdelilah Karara , Mohamed Rossafi

In this paper, we give some results concerning atomic decompositions for operators on reproducing kernel Hilbert spaces, using frame theory techniques. We provide also generalizations for atomic decompositions of some theorems for…

Functional Analysis · Mathematics 2014-02-03 Laura Gavruta

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.

Operator Algebras · Mathematics 2018-11-13 Mohamed Rossafi , Samir Kabbaj

k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by…

Functional Analysis · Mathematics 2019-01-15 Gholamreza Rahimlou , Reza Ahmadi , Mohammad Ali Jafarizadeh , Susan Nami

Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g-fusion frame…

Operator Algebras · Mathematics 2021-12-10 Fakhr-dine Nhari , Mohamed Rossafi