Construction of g-fusion frames in Hilbert spaces

2020 ◽  
Vol 23 (02) ◽  
pp. 2050015
Author(s):  
Vahid Sadri ◽  
Gholamreza Rahimlou ◽  
Reza Ahmadi ◽  
Ramazan Zarghami Farfar
Keyword(s):  
Hilbert Spaces ◽  
Closed Range ◽  
Fusion Frames ◽  
Interesting Topic ◽  
Fusion Frame

After introducing g-frames and fusion frames by Sun and Casazza, respectively, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce a Parseval g-fusion frame.

FUSION FRAMES AND g-FRAMES IN HILBERT C*-MODULES

2008 ◽  
Vol 06 (03) ◽  
pp. 433-446 ◽  
Author(s):  
AMIR KHOSRAVI ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
Frame Theory ◽  
Fusion Frames ◽  
Perturbation Result ◽  
Fusion Frame

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g-frames. In this paper, we introduce fusion frames and g-frames in Hilbert C*-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g-frames in Hilbert spaces. We also show that tensor product of fusion frames (g-frames) is a fusion frame (g-frame) and tensor product of resolution of identity is a resolution of identity.

scholarly journals Controlled K-Fusion Frame for Hilbert Spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 116-133
Author(s):  
Nadia Assila ◽  
Samir Kabbaj ◽  
Brahim Moalige
Keyword(s):  
Hilbert Spaces ◽  
Frame Theory ◽  
Stability Conditions ◽  
Fusion Frames ◽  
Controlled Fusion ◽  
Fusion Frame

AbstractK-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled K-fusion frames, and we develop some results on the controlled K-fusion frames for Hilbert spaces, which generalize some well known results of controlled fusion frame case. Also we discuss some characterizations of controlled Bessel K-fusion sequences and of controlled K-fusion frames. Further, we analyze stability conditions of controlled K-fusion frames under perturbation.

scholarly journals Weaving K-fusion frames in hilbert spaces

2020 ◽  
Vol 3 (2) ◽  
pp. 101-116
Author(s):  
Hanbing Liu ◽  
◽  
Yongdong Huang ◽  
Chongjun Li ◽  
◽  
...  
Keyword(s):  
Hilbert Spaces ◽  
Fusion Frames

scholarly journals Characterization and Construction of K-Fusion Frames and Their Duals in Hilbert Spaces

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
Fahimeh Arabyani Neyshaburi ◽  
Ali Akbar Arefijamaal
Keyword(s):  
Hilbert Spaces ◽  
Fusion Frames

Operators with Closed Range, Pseudo-Inverses, and Perturbation of Frames for a Subspace

1999 ◽  
Vol 42 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Ole Christensen
Keyword(s):  
Recent Work ◽  
Hilbert Spaces ◽  
Bounded Operator ◽  
Closed Range ◽  
The Stability

AbstractRecent work of Ding and Huang shows that if we perturb a bounded operator (between Hilbert spaces) which has closed range, then the perturbed operator again has closed range. We extend this result by introducing a weaker perturbation condition, and our result is then used to prove a theorem about the stability of frames for a subspace.

(F,G)-operator frames for ℒ(ℋ,𝒦)

2020 ◽  
Vol 18 (05) ◽  
pp. 2050031
Author(s):  
J. Sedghi Moghaddam ◽  
A. Najati ◽  
F. Ghobadzadeh
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Bounded Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Atomic Systems ◽  
Pseudo Inverse

The concept of [Formula: see text]-frames was recently introduced by Găvruta7 in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Let [Formula: see text] be a unital [Formula: see text]-algebra, [Formula: see text] be finitely or countably generated Hilbert [Formula: see text]-modules, and [Formula: see text] be adjointable operators from [Formula: see text] to [Formula: see text]. In this paper, we study a class of [Formula: see text]-bounded operators and [Formula: see text]-operator frames for [Formula: see text]. We also prove that the pseudo-inverse of [Formula: see text] exists if and only if [Formula: see text] has closed range. We extend some known results about the pseudo-inverses acting on Hilbert spaces in the context of Hilbert [Formula: see text]-modules. Further, we also present some perturbation results for [Formula: see text]-operator frames in [Formula: see text].

scholarly journals Quantum Optimal Control for Bose-Einstein-Condensates at Complex Space

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Hilbert Spaces ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Complex Space ◽  
Pitaevskii Equation ◽  
Interesting Topic ◽  
Quantum Optimal Control ◽  
Control Target ◽  
Bose Einstein

Quantum control of Bose-Einstein-Condensates is interesting topic in the areas of control and physics. In this work, Gross-Pitaevskii equation expressed Bose-Einstein-Condensates is considered as control target. Full theoretical proof for the existence of quantum optimal control is provided for cubical Schrodinger equation in complex Hilbert spaces.

Controlled g-fusion frame in Hilbert space

2021 ◽  
pp. 2150009
Author(s):  
Hanbing Liu ◽  
Yongdong Huang ◽  
Fengjuan Zhu
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Iterative Algorithms ◽  
Bessel Sequence ◽  
Numerical Efficiency ◽  
Fusion Frames ◽  
Controlled Fusion ◽  
Fusion Frame

Fusion frame is a generalization of frame, which can analyze signals by projecting them onto multidimensional subspaces. Controlled fusion frame as generalization of fusion frame, it can improve the numerical efficiency of iterative algorithms for inverting the fusion frame operators. In this paper, we first introduce the notion of controlled g-fusion frame, discuss several properties of controlled g-fusion Bessel sequence. Then, we present some sufficient conditions and some characterizations of controlled g-fusion frames. Finally, we study the sum of controlled g-fusion frames.

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