Stability of dual $g$-fusion frames in Hilbert spaces

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.

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

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691308002458 ◽

2008 ◽

Vol 06 (03) ◽

pp. 433-446 ◽

Cited By ~ 20

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.

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Some results about operator perturbation of fusion frames in Hilbert spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.07.068 ◽

2015 ◽

Vol 421 (2) ◽

pp. 1417-1427 ◽

Cited By ~ 7

Author(s):

Xue-Bin Li ◽

Shou-Zhi Yang ◽

Yu-Can Zhu

Keyword(s):

Hilbert Spaces ◽

Fusion Frames

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Block sequences and g-frames

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691315500095 ◽

2015 ◽

Vol 13 (02) ◽

pp. 1550009

Author(s):

Renu Chugh ◽

S. K. Sharma ◽

Shashank Goel

Keyword(s):

Hilbert Spaces ◽

Operator Theory ◽

American Mathematical Society ◽

Mathematical Society ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Block Sequence ◽

Fusion Frames ◽

Frame System ◽

Necessary And Sufficient

Casazza and Kutyniok [Frames of subspaces, in Wavelets, Frames and Operator Theory, Contemporary Mathematics, Vol. 345 (American Mathematical Society, Providence, RI, 2004), pp. 87–113] defined fusion frames in Hilbert spaces to split a large frame system into a set of (overlapping) much smaller systems and being able to process the data effectively locally within each sub-system. In this paper, we handle this problem using block sequences and generalized block sequences with respect to g-frames. Examples have been given to show their existence. A necessary and sufficient condition for a block sequence with respect to a g-frame to be a g-frame has been given. Finally, a sufficient condition for a generalized block sequence with respect to a g-frame to be a g-frame has been given.

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On some new inequalities for fusion frames in Hilbert spaces

Mathematical Inequalities & Applications ◽

10.7153/mia-20-56 ◽

2017 ◽

pp. 889-900

Author(s):

Dong ei Li ◽

Jins ng Leng

Keyword(s):

Hilbert Spaces ◽

Fusion Frames ◽

New Inequalities

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Subfusion Frames

Abstract and Applied Analysis ◽

10.1155/2012/603580 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12

Author(s):

Z. Amiri ◽

M. A. Dehghan ◽

E. Rahimi

Keyword(s):

Hilbert Spaces ◽

Fusion Frames ◽

New Construction

Fusion frames are generalizations of frames in Hilbert spaces which were introduced by Casazza et al. (2008). In the present paper, we study the relations between fusion frames and subfusion frame operators. Specially, we introduce new construction of subfusion frames and derive new results.

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Continuous weaving fusion frames in Hilbert spaces

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691320500356 ◽

2020 ◽

Vol 18 (05) ◽

pp. 2050035

Author(s):

Vahid Sadri ◽

Reza Ahmadi ◽

Gholamreza Rahimlou

Keyword(s):

Linear Operator ◽

Hilbert Spaces ◽

Bounded Linear Operator ◽

Sufficient Condition ◽

Bounded Linear ◽

Fusion Frames

In this paper, we first introduce the notation of weaving continuous fusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving [Formula: see text]-fusion frames under the bounded linear operator and also, removing vectors from these frames, we will present a necessarily and sufficient condition about [Formula: see text]-woven and [Formula: see text]-fusion woven. Finally, perturbation of these frames will be introduced.

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