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Related papers: Controlled $K$-frames in Hilbert $C^*$-modules

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In the present paper, we introduce the notion of controlled $E$-frames. Then we investigate and study some properties of them and characterize all controlled $E$-duals associated with a given controlled $E$-frame.

Functional Analysis · Mathematics 2024-05-10 H. Hedayatirad , T. L. Shateri

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

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

In this paper, we study perturbation of Hilbert-Schmidt frames under structured modifications, where the perturbation takes the form of replacing finitely or infinitely many frame elements. We establish explicit criteria under which the…

Functional Analysis · Mathematics 2026-05-13 Jyoti , Lalit Kumar Vashisht

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

K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…

Functional Analysis · Mathematics 2017-05-30 Fahimeh Arabyani Neyshaburi , Ghadir Mohajeri Minaei , Ehsan Anjidani

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

In this paper, we present controlled finite continuous frames in a finite dimensional Hilbert space and we study some properties of them. Parseval controlled integral frames are presented and we characterize operators that construct…

Functional Analysis · Mathematics 2023-10-11 Hafida Massit , Mohamed Rossafi , Choonkil Park

In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from Hilbert $C^{\ast}$-modules $\mathcal{H}$ to it self noted $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some propertis…

Functional Analysis · Mathematics 2020-12-02 Hatim Labrigui , Samir Kabbaj

In this paper, we investigate some characterizations of dual continuous frames and give some results about them. Also, we refer to the method of constructing a family of duals through a fixed dual and show there exists a one-to-one…

Functional Analysis · Mathematics 2023-02-28 H. Ghasemi , T. L. Shateri , A. Arefijamaal

Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept…

Functional Analysis · Mathematics 2024-05-28 M. Firouzi Parizi , A. Alijani , M. A. Dehghan

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

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

In this article, we study tensor product of Hilbert $C^*$-modules and Hilbert spaces. We show that if $E$ is a Hilbert $A$-module and $F$ is a Hilbert $B$-module, then tensor product of frames (orthonormal bases) for $E$ and $F$ produce…

Operator Algebras · Mathematics 2007-05-23 Amir Khosravi , Behrooz Khosravi

Hilbert C*-modules are the analogues of Hilbert spaces where a C*-algebra plays the role of the scalar field. With the advent of Kasparov's celebrated KK-theory they became a standard tool in the theory of operator algebras. While the…

Operator Algebras · Mathematics 2016-12-23 Jens Kaad , Matthias Lesch

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

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…

Functional Analysis · Mathematics 2024-02-15 Abdelilah Karara , Mohamed Rossafi

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

In this paper, we characterize and study the concept of controlled continuous $g$-frame which is an extension of continuous $g$-frame in Hilbert spaces. We introduce the concept of controlled continuous dual $g$-frame and observe some…

Functional Analysis · Mathematics 2022-10-25 Mohamed Rossafi , Fakhr-dine Nhari , P. Sam Johnson

In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.

Functional Analysis · Mathematics 2024-11-27 H. Hedayatirad , T. L. Shateri