On Some New Inequalities For Continuous Fusion Frames in Hilbert Spaces

2018 ◽  
Vol 15 (4) ◽  
Author(s):  
Dongwei Li ◽  
Jinsong Leng
Keyword(s):  
Hilbert Spaces ◽  
Fusion Frames ◽  
New Inequalities

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

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.

scholarly journals Some New Inequalities for Dual Continuous g-Frames

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 662 ◽  
Author(s):  
Yan-Ling Fu ◽  
Wei Zhang
Keyword(s):  
Hilbert Spaces ◽  
Upper Bound ◽  
New Inequalities

In the present paper, we establish new inequalities for dual continuous generalized frames by adopting operator methods. The inequalities are parameterized by the parameter λ ∈ R . These results generalize those obtained by Balan, Casazza and Găvruţa and cover recently obtained results by Zhang and Li in [Zhang, W.; Li, Y.Z. New inequalities and erasures for continuous g-frames. Math. Rep. 2018, 20, 263–278]. Moreover, we also give an upper bound of inequality for alternate continuous generalized frames in Hilbert spaces. It differs from previous results.

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 New bounds for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 27-39 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Selfadjoint Operators ◽  
Čebyšev Functional ◽  
Subject Classifications ◽  
Mathematics Subject Classifications ◽  
New Inequalities

Some new inequalities for the Cebysev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are given. 2010 Mathematics Subject Classifications. 47A63; 47A99. .

scholarly journals More on Inequalities for Weaving Frames in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 141 ◽  
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Hilbert Spaces ◽  
Operator Theory ◽  
Triangle Inequality ◽  
Bounded Operator ◽  
Point Of View ◽  
Real Numbers ◽  
Linear Bounded Operator ◽  
Bessel Sequences ◽  
New Inequalities

In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real numbers. It is indicated that our results are more general and cover the corresponding results recently obtained by Li and Leng. We also give a triangle inequality for weaving frames in Hilbert spaces, which is structurally different from previous ones.

scholarly journals Some results about operator perturbation of fusion frames in Hilbert spaces

2015 ◽  
Vol 421 (2) ◽  
pp. 1417-1427 ◽  
Author(s):  
Xue-Bin Li ◽  
Shou-Zhi Yang ◽  
Yu-Can Zhu
Keyword(s):  
Hilbert Spaces ◽  
Fusion Frames
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