arXiv subjects

Abdelilah Karara

Publications and source records attributed to Abdelilah Karara.

10 recordsLinked to original sources

arXiv2025

Continuous biframes in Hilbert $C^{\ast}-$modules

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 study continuous biframe Bessel multiplier and dual continuous biframe in Hilbert $ C^{\ast}- $modules. Also, we develop the concept of continuous biframes in the tensor product of two Hilbert $C^{\ast}$-modules over a unital $C^{\ast}$-algebra $\mathcal{A}$ and provide some properties of invertible transformed biframes and Bessel multipliers in the tensor product.

math.FA↗

arXiv2025

Sum of $g-$frames in Hilbert $C^{\ast}-$modules

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 perturbations and provide illustrative examples in the context of $C^*$-algebras. Our results unify and extend many of the existing theorems on g-frames, focusing on the invertibility of associated operators as a key condition for guaranteeing that sums of g-frames preserve the g-frame property.

math.FA↗

arXiv2025

Biframes in Hilbert $C^{\ast}-$modules

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 operator theory by establishing some properties of biframes in Hilbert $ C^{\ast}- $modules.

math.FA↗

arXiv2024

Continuous bi-g-frames for operators in Hilbert spaces

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 several results about the stability of continuous bi-g-Bessel sequence and K-bi-g-frame are produced via the use of frame theory methods.

math.FA↗

arXiv2024

Continuous K-biframes in Hilbert spaces

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 establishing various properties.

math.FA↗

arXiv2024

K-bi-g-frames in Hilbert spaces

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 are produced via the use of frame theory methods.

math.FA↗

arXiv2024

K-biframes in Hilbert spaces

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 theory by establishing various relationships and properties.

math.FA↗

arXiv2024

Construction of continuous K-g-Frames in Hilbert $C^{\ast}$-Modules

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 continuous K-g-frames can be retrieved from those that already exist. Additionally, we discuss the sum of continuous K-g-frames, discover some of their characterizations, and offer some adjointable operators to construct new continuous K-g-frames from the previous ones.

math.FA↗

arXiv2023

Bessel sequences in Hilbert $C^{\ast}$-modules

In this peaper we stady certain Bessel sequences $\left\{f_k\right\}_{k=1}^{\infty}$ in Hilbert C*- modules $\mathcal{H}$ for which operator $S$ defined by \ref{eq2} is of the form $\mathcal{T}+ξI$, for some real number $ξ$ and a adjointable linear operator $\mathcal{T}$. Additionally, we investigate frames known as compact-tight frames, which have frame operators that are compact perturbations of constant multiples of the identity. As a conclusion, we provide a theory regarding the weaving of specific compact-tight frames.

math.FA↗

arXiv2023

Representations of $g$-fusion frames in Hilbert $C^{\ast}$-Modules

In this paper, we provide some generalization of the concept of fusion frames following that evaluate their representability via a linear operator in Hilbert $C*$-module. We assume that $Υ_ξ$ is self-adjoint and $Υ_ξ(\frak{N} _ξ)= \frak{N} _ξ$ for all $ξ\in \mathfrak{S}$, and show that if a $g-$fusion frame $\{(\frak{N} _ξ, Υ_ξ)\}_{ξ\in \mathfrak{S}}$ is represented via a linear operator $\mathcal{T}$ on $\hbox{span} \{\frak{N} _ξ\}_{ ξ\in \mathfrak{S}}$, then $\mathcal{T}$ is bounded. Moreover, if $\{(\frak{N} _ξ, Υ_ξ)\}_{ξ\in \mathfrak{S}}$ is a tight $g-$fusion frame, then $Υ_ξ$ is not represented via an invertible linear operator on $\hbox{span}\{\frak{N} _ξ\}_{ξ\in \mathfrak{S}}$, We show that, under certain conditions, a linear operator may also be used to express the perturbation of representable fusion frames. Finally, we'll investigate the stability of this fusion frame type.

math.FA↗