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Related papers: Continuous frames in Hilbert C*-modules

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In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert $C^*$-modules. We extend the Casazza-Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert…

Functional Analysis · Mathematics 2023-05-23 Hadi Ghasemi , Tayebe Lal Shateri

Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…

Functional Analysis · Mathematics 2020-11-25 Mohamed Rossafi , Brahim Moalige , Hamid Faraj , Abdeslam Touri , Samir Kabbaj

Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames…

Functional Analysis · Mathematics 2021-01-13 A. Touri

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

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

Frame theory has been rapidly generalized and various generalizations have been developed. In this paper, we present a brief survey of the frames in Hilbert $C^{\ast}$-modules, including frames, $\ast$-frames, g-frames, $\ast$-g-frames,…

Functional Analysis · Mathematics 2022-12-20 M'hamed Ghiati , Mohammed Mouniane , 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

We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…

Functional Analysis · Mathematics 2023-09-15 Prasenjit Ghosh , T. K. Samanta

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

In this present paper we introduce weaving Hilbert space frames in the continuous case, we give new approaches for manufacturing pairs of woven continuous frames and we obtain new properties in continuous weaving frame theory related to…

Functional Analysis · Mathematics 2023-05-08 Hafida Massit , 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

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 view some fundamentals of the theory of Hilbert C*-modules and examine some ways in which Hilbert C*-modules differ from Hilbert spaces.

Operator Algebras · Mathematics 2008-08-21 Mohammad Sal Moslehian

We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…

Functional Analysis · Mathematics 2024-03-07 Prasenjit Ghosh , T. K. Samanta

In this paper, we present the concept of continuous biframes in a Hilbert space. We examine the essential properties of biframes with an emphasis on the biframe operator. Moreover, we introduce a new type of Riesz bases, referred to as…

Functional Analysis · Mathematics 2023-12-13 Hafida Massit , Roumaissae Eljazzar , Mohamed Rossafi

In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will…

Functional Analysis · Mathematics 2017-06-14 Asghar Rahimi , Zahra Darvishi , Bayaz Daraby

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

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

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

Frames play significant role in various areas of science and engineering. In this paper, we introduce the concepts of frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H, K})$ and their generalizations. Moreover, we obtain some new results for…

Operator Algebras · Mathematics 2019-07-05 Mohamed Rossafi , Samir Kabbaj