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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 Balazs, Antoine and Grybos in Hilbert spaces to…

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

In this paper, we introduce the concept of Continuous $\ast$-K-g-Frame in Hilbert $C^{\ast}$-Modules and we give some properties.

Operator Algebras · Mathematics 2019-09-17 Abdeslam Touri , Mohamed Rossafi , Hatim Labrigui , Abdellatif Akhlidj

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

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…

Operator Algebras · Mathematics 2017-05-02 Mehdi Rashidi-Kouchi , Asghar Rahimi

In this paper, we will introduce the new concepts of continuous bi-g-frames and continuous K-bi-g-frame for Hilbert spaces. Then, we examine some characterizations properties with the help of a biframe operator. Finally, we investigate…

Functional Analysis · Mathematics 2024-04-16 Abdelilah Karara , Mohamed Rossafi

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

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

We study the stability of Fredholm property for regular operators on Hilbert $C^*$-modules under some certain perturbations. We treat this problem when perturbing operators are (relatively) bounded or relatively compact. We also consider…

Operator Algebras · Mathematics 2017-02-21 Marzieh Forough

In this article, we study g-frames in Hilbert $C^*$-modules and investigate conditions under which the sum of two g-frames (or a g-frame and a g-Bessel sequence) remains a g-frame. We also address the stability of g-frames under certain…

Functional Analysis · Mathematics 2025-02-19 Abdellatif Lfounoune , Hafida Massit , Abdelilah Karara , Mohamed Rossafi

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

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 the present paper, we investigate some properties of duals of continuous frames in Hilbert C*-modules. In particular, we give requirements so that by removing some elements of a continuous frame, it does not remain a continuous frame and…

Functional Analysis · Mathematics 2023-04-25 Hadi Ghasemi , Tayebe Lal Shateri

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 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…

Functional Analysis · Mathematics 2021-11-19 Roumaissae Eljazzar , 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

Frame theory has a great revolution in recent years. This new Theory have been extended from Hilbert spaces to Hilbert C*-modules. In this paper, we introduce the notion of dual *-K-g-frames in Hilbert A-modules. Lastly we study…

Operator Algebras · Mathematics 2021-10-01 M'hamed Ghiati , Samir Kabbaj , Hatim Labrigui , Abdeslam Touri , Mohamed Rossafi

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that…

Functional Analysis · Mathematics 2013-12-13 Dongyang Chen , Lei Li , Bentuo Zheng

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

In this work, we provide some constructions and the sum of new continuous K-g-frames in Hilbert$C^{\ast}$-Modules. We provide certain necessary and sufficient conditions for some adjointable operators on $\mathcal{H}$, under which new…

Functional Analysis · Mathematics 2024-02-06 Abdelilah Karara , Mohamed Rossafi , Mohammed Klilou , Samir Kabbaj

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