Related papers: Some generalizations of K-g-frames in Hilbert $C^{…
In this paper, we introduce the concept of $K$-fusion frames and propose the duality for such frames. The relation between the local frames of $K$-fusion frames with their dual is studied. The elements from the range of a bounded linear…
We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven…
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…
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…
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…
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…
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…
In the present paper the notion of continuous frames is introduced and some results of these frames are proved. Next, we give the concept of duals of continuous frames in Hilbert C*-modules and investigate some properties of them.
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
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…
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear…
In this paper we present results concerning orthogonality in Hilbert $C^*$-modules. Moreover, for a $C^*$-algebra $\mathscr{A}$, we prove theorems concerning the multi-$\mathscr{A}$-linearity and its preservation by $\mathscr{A}$-linear…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We classify the $(\mathfrak{g},K)$-modules generated by nearly holomorphic Hilbert-Siegel modular forms by the global method. As an application, we study the image of projection operators on the space of nearly holomorphic Hilbert-Siegel…
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…
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.
The conditions for sequences $\{f_{k}\}_{k=1}^{\infty}$ and $\{g_{k}\}_{k=1}^{\infty}$ being Bessel sequences, frames or Riesz bases, can be expressed in terms of the so-called cross-Gram matrix. In this paper we investigate the cross-Gram…
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…
We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct…
Operator-valued frame ($G$-frame), as a generalization of frame is introduced by Kaftal, Larson, and Zhang in \textit{Trans. Amer. Math. Soc.}, 361(12):6349-6385, 2009 and by Sun in \textit{J. Math. Anal. Appl.}, 322(1):437-452, 2006. It…