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Related papers: *-Frames for operators on Hilbert modules

200 papers

In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this…

Functional Analysis · Mathematics 2023-10-31 Giorgia Bellomonte , Rosario Corso

The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in…

Functional Analysis · Mathematics 2024-11-08 Najib Khachiaa

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

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson

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

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 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.

Functional Analysis · Mathematics 2023-01-24 Hadi Ghasemi , Tayebe Lal Shateri

In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful…

Functional Analysis · Mathematics 2019-12-03 Animesh Bhandari , Debajit Borah , Saikat Mukherjee

We present the notion of continuous controlled K-g-fusion frame in Hilbert space which is the generalization of discrete controlled K-g-fusion frame. We discuss some characterizations of continuous controlled K-g-fusion frame. Relationship…

Functional Analysis · Mathematics 2024-10-16 Prasenjit Ghosh , T. K. Samanta

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

We introduce the notion of a g-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of g-fusion frames. Also we shall describe the concept of…

Functional Analysis · Mathematics 2024-03-12 Prasenjit Ghosh , T. K. Samanta

A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The basic tools of frame theory are described in the formalism of Krein spaces. It is…

Functional Analysis · Mathematics 2013-04-10 Kevin Esmeral , Osmin Ferrer , Elmar Wagner

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

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and…

Functional Analysis · Mathematics 2012-04-09 Asghar Rahimi , Abolhassan Fereydooni

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

Concept of a family of local atoms in n-Hilbert space is being studied. K-frame in tensor product of n-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of n-Hilbert spaces is presented and…

Functional Analysis · Mathematics 2023-03-29 Prasenjit Ghosh , T. K. Samanta

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

Controlled frames in Hilbert spaces have been introduced by Balazs, Antoine and Grybos to improve the numerical output of in relation to algorithms for inverting the frame operator. In this paper we have introduced and displayed some new…

Functional Analysis · Mathematics 2018-05-02 Habib shakoory , Reza Ahmadi , Naghi Behzadi , Susan Nami

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 this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. We define cg-orthonormal bases for a Hilbert space H and verify their properties and relations with cg-frames. Actually, we present that every…

Functional Analysis · Mathematics 2019-05-20 Morteza Rahmani