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

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In this paper, we will introduce the concept of a continuous biframe for Hilbert $ C^{\ast}- $modules. Then, we examine some characterizations of this biframe with the help of an invertible and adjointable operator is given. Moreover, we…

Functional Analysis · Mathematics 2025-03-24 Abdellatif Lfounoune , Abdelilah Karara , Mohamed Rossafi

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 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

Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the…

Functional Analysis · Mathematics 2024-01-03 Hafida Massit , Mohamed Rossafi , Choonkil Park

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded…

Operator Algebras · Mathematics 2008-02-18 Michael Frank , Vern I. Paulsen

The concept of a bi-g-fusion frame for a Hilbert space, which is a generalizations of a controlled g-fusion frame, is introduced and an example is given. Finally, bi-g-fusion frame in tensor product of Hilbert spaces is considered.

Functional Analysis · Mathematics 2024-11-05 Prasenjit Ghosh , T. K. Samanta

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

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 study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…

Functional Analysis · Mathematics 2017-06-26 Anirudha Poria

In this paper, we introduce the concept of Continuous $\ast$-g-Frame in Hilbert $C^{\ast}$-Modules and we establish some results. We also discuss the stability problem for Continuous $\ast$-g-Frame.

Operator Algebras · Mathematics 2019-12-30 Mohamed Rossafi , Samir 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 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 introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames.…

Functional Analysis · Mathematics 2020-11-06 Anirudha Poria

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

Due to the importance of frame representation by a bounded operator in dynamical sampling, researchers studied the frames of the form $\{T^{i-1} f\}_{i\in \mathbb{N}}$, which $f$ belongs to separable Hilbert space $\mathcal{H}$ and $T\in…

Functional Analysis · Mathematics 2020-05-12 Fatemeh Ghobadzadeh , Yavar Khedmati , Javad Sedghi Moghaddam

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form $\{T^i f_1\}_{i\in \mathbb{N}}$, where $f_1$ belongs to Hilbert space $\h$ and $T:\h\rightarrow\h$ belongs to certain classes of the…

Functional Analysis · Mathematics 2018-12-04 Yavar Khedmati , Fatemeh Ghobadzadeh

In the present paper, we introduce the notion of $E$-$g$-frames for a separable Hilbert spaces $\mathcal H$, where $E$ is an invertible infinite matrix mapping on the Hilbert space $\mathop\oplus\limits_{n=1}^{\infty}\mathcal H_n$. We study…

Functional Analysis · Mathematics 2024-01-10 H. Hedayatirad , T. L. Shateri

In this paper, firstly we investigate conditions under which the action of an operator on a $K$-frame, remain again a $K$-frame for Hilbert module E. We also give a generalization of Douglas Theorem and we shall use it to prove the sum of…

Operator Algebras · Mathematics 2018-02-07 Gh. Abbaspour Tabadkan , A. A. Arefijamaal , M. Mahmoudieh

In this paper, we define the concept of soft $g$-frame in soft Hilbert spaces by extending the concept of soft from frame to $g$-frame. We then show some properties of the soft $g$-frames in soft Hilbert spaces. Among other results, we show…

Functional Analysis · Mathematics 2024-08-27 Sayyed Mehrab Ramezani

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