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Joint Similarities and Parameterizations for Dilations of Dual g-frame Pairs in Hilbert Spaces

Xun Xiang Guo

Acta Mathematica Sinica, English Series > 2019 > 35 > 11 > 1827-1840

In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense...

article

Continuous K-g-Frames in Hilbert Spaces

E. Alizadeh, A. Rahimi, E. Osgooei, M. Rahmani

Bulletin of the Iranian Mathematical Society > 2019 > 45 > 4 > 1091-1104

In this paper, we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames in Hilbert spaces. Moreover, we define the related operators of c-K-g-frames. Then, we give necessary and sufficient conditions on c-K-g-frames to characterize them. Finally, we verify the perturbation of c-K-g-frames.

article

Characterization and stability of approximately dual g-frames in Hilbert spaces

Yan-Ling Fu, Wei Zhang

Journal of Inequalities and Applications > 2018 > 2018 > 1 > 1-13

This paper addresses approximately dual g-frames. First, we establish a connection between approximately dual g-frames and dual g-frames and obtain a characterization of approximately dual g-frames. Second, we give results on stability of approximately dual g-frames, which cover the results obtained by other authors.

article

Some Results on Fusion Frames and g-Frames

Nguyen Quynh Nga

Results in Mathematics > 2018 > 73 > 2 > 1-19

In this paper, we discuss some aspects where fusion frames and g-frames behave differently from frames. Several counterexamples to make clear their different behaviour are given. We also improve some results on g-frames. Moreover, we extend the notion of redundancy to g-frames and show that most of the desirable properties of lower and upper redundancies on frames and fusion frames can carry over...

article

-g-frames in tensor products of Hilbert C-modules

Mohamed Rossafi, Samir Kabbaj

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2018 > 17

article

New double inequalities for g-frames in Hilbert $$C^{*}$$ C ∗ -modules

Zhong-Qi Xiang

SpringerPlus > 2016 > 5 > 1 > 1-8

In this work, we establish two types of double inequalities for g-frames in Hilbert $$C^{*}$$ C ∗ -modules, which involve scalars $$\lambda \in [0,1]$$ λ ∈ [ 0 , 1 ] and $$\lambda \in [\frac{1}{2},1]$$ λ ∈ [ 1 2 , 1 ] respectively. It is shown that the results we obtained can immediately lead to the existing corresponding results when taking $$\lambda =\frac{1}{2}$$...

article

Approximate duality of g-frames in Hilbert spaces

Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI

Acta Mathematica Scientia > 2014 > 34 > 3 > 639-652

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We...

article

Some equalities and inequalities for g-Bessel sequences in Hilbert spaces

Jian-Zhen Li, Yu-Can Zhu

Applied Mathematics Letters > 2012 > 25 > 11 > 1601-1607

G-frames have some properties similar to those of frames in complex Hilbert spaces, but not all of their properties are similar. Some authors have extended the equalities and inequalities for frames and dual frames to g-frames and dual g-frames in Hilbert spaces, respectively. In this work, we give some new equalities and inequalities for g-Bessel sequences in Hilbert spaces with pseudo-inverse operators...

article

Exact g-frames in Hilbert spaces

Jian-Zhen Li, Yu-Can Zhu

Journal of Mathematical Analysis and Applications > 2011 > 374 > 1 > 201-209

G-frames, which were considered recently as generalized frames in Hilbert spaces, have many properties similar to those of frames, but not all the properties are similar. For example, exact frames are equivalent to Riesz bases, but exact g-frames are not equivalent to g-Riesz bases. In this paper, we firstly give a characterization of an exact g-frame in a complex Hilbert space. We also obtain an...

chapter

The unified condition for stability of g-frames

Deng-Feng Li, Li-Jun Yang, Guo-chang Wu

2010 3rd International Conference on Advanced Computer Theory and Engineering(ICACTE) > 4 > V4-305 - V4-308

2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 2010)

In this paper, the unified condition for stability of g-frames is established, and it is shown that the obtained results cover the existing results. The stability of g-Riesz bases is also established.

article

Some properties of g-frames in Hilbert C∗-modules

Xiang-Chun Xiao, Xiao-Ming Zeng

Journal of Mathematical Analysis and Applications > 2010 > 363 > 2 > 399-408

In this paper we give some new results for g-frames in Hilbert C∗-modules and then we introduce a bounded A-linear operator L, by means of this operator L we character the properties of the g-frames and g-Riesz basis in Hilbert C∗-modules. Finally, we establish some important equalities and inequalities for frames and g-frames in Hilbert C∗-modules.

article

g-Besselian frames in Hilbert spaces

Ming Ling Ding, Yu Can Zhu

Acta Mathematica Sinica, English Series > 2010 > 26 > 11 > 2117-2130

In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame...

article

G-frames and g-frame sequences in Hilbert spaces

Yan Jin Wang, Yu Can Zhu

Acta Mathematica Sinica, English Series > 2009 > 25 > 12 > 2093-2106

In this paper, we first determine the relations among the best bounds A and B of the g-frame, the g-frame operator S and the pre-frame operator Q and give a necessary and sufficient condition for a g-frame with bounds A and B in a complex Hilbert space. We also introduce the definition of a g-frame sequence and obtain a necessary and sufficient condition for a g-frame sequence with bounds A and B...

article

Characterizations of g-frames and g-Riesz bases in Hilbert spaces

Yu Can Zhu

Acta Mathematica Sinica, English Series > 2008 > 24 > 10 > 1727-1736

In this paper, we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space, which will play a key role in studying g-frames and g-Riesz bases etc. Using the pre-frame operator Q, we give some necessary and sufficient conditions for a g-Bessel sequence, a g-frame, and a g-Riesz basis in a complex Hilbert space, which have properties similar to those of the Bessel sequence, frame,...

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Search results

Joint Similarities and Parameterizations for Dilations of Dual g-frame Pairs in Hilbert Spaces

Continuous K-g-Frames in Hilbert Spaces

Characterization and stability of approximately dual g-frames in Hilbert spaces

Some Results on Fusion Frames and g-Frames

-g-frames in tensor products of Hilbert C-modules

New double inequalities for g-frames in Hilbert $$C^{*}$$ C ∗ -modules

Approximate duality of g-frames in Hilbert spaces

Some equalities and inequalities for g-Bessel sequences in Hilbert spaces

Exact g-frames in Hilbert spaces

The unified condition for stability of g-frames

Some properties of g-frames in Hilbert C∗-modules

g-Besselian frames in Hilbert spaces

G-frames and g-frame sequences in Hilbert spaces

Characterizations of g-frames and g-Riesz bases in Hilbert spaces

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