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.

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.

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.

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.

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

scholarly journals Approximative K-atomic decompositions and frames in Banach spaces

2018 ◽  
Vol 26 (1/2) ◽  
pp. 153-166
Author(s):  
Shah Jahan
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Atomic Decomposition ◽  
Necessary Conditions ◽  
Bounded Operator ◽  
Special Kind ◽  
Frame Theory ◽  
Bessel Sequence ◽  
Atomic Decompositions ◽  
Counter Example

L. Gǎvruţa (2012) introduced a special kind of frames, named K-frames, where K is an operator, in Hilbert spaces, which is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative K-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative K-atomic decompositions in Banach spaces. Also some results on the existence of approximative K-atomic decompositions are obtained. We discuss several methods to construct approximative K-atomic decomposition for Banach Spaces. Further, approximative d-frame and approximative d-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative d-Bessel sequence and approximative d-frame give rise to a bounded operator with respect to which there is an approximative K-atomic decomposition. Example and counter example are provided to support our concept. Finally, a possible application is given.

scholarly journals Some New Characterizations andg-Minimality and Stability ofg-Bases in the Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xunxiang Guo
Keyword(s):  
Hilbert Spaces ◽  
Frame Theory ◽  
Schauder Basis ◽  
Simple Condition ◽  
Similar Role ◽  
Perturbation Result

The concept ofg-basis in the Hilbert spaces is introduced by Guo (2012) who generalizes the Schauder basis in the Hilbert spaces.g-basis plays the similar role ing-frame theory to that the Schauder basis plays in frame theory. In this paper, we establish some important properties ofg-bases in the Hilbert spaces. In particular, we obtain a simple condition under which some important properties established in Guo (2012) are still true. With these conditions, we also establish some new interesting properties ofg-bases which are related tog-minimality. Finally, we obtain a perturbation result aboutg-bases.

scholarly journals PERTURBATION OF FRAMES IN BANACH SPACES

2012 ◽  
Vol 05 (01) ◽  
pp. 1250011 ◽  
Author(s):  
Diana T. Stoeva
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Stability Conditions ◽  
Tight Frames ◽  
Sharp Bounds

In this paper we consider perturbation of several frame-concepts in separable Banach spaces. We determine stability conditions with sharp bounds and discuss the necessity of some of them. Further, we investigate equivalence between several perturbation conditions. In particular, a result for tight frames for Hilbert spaces is obtained.

scholarly journals Some results about g-frames in Hilbert spaces

2022 ◽  
Vol 355 ◽  
pp. 02001
Author(s):  
Lan Luo ◽  
Jingsong Leng ◽  
Tingting Xie
Keyword(s):  
Hilbert Spaces ◽  
Natural Extension ◽  
Linear Operators ◽  
Frame Theory ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Operator Spectrum ◽  
The Relationship

The concept of g-frame is a natural extension of the frame. This article mainly discusses the relationship between some special bounded linear operators and g-frames, and characterizes the properties of g-frames. In addition, according to the operator spectrum theory, the eigenvalues are introduced into the g-frame theory, and a new expression of the best frame boundary of the g-frame is given.

Sign in / Sign up

Export Citation Format

Share Document