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

Characterization and Construction of K-Fusion Frames and Their Duals in Hilbert Spaces K-frames, a new generalization of frames, were recently considered by L. G $$\breve{\text {a}}$$ a ˘ vruţa in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a variety of applications. In the present paper, we introduce the notion of K-fusion frames in Hilbert spaces and obtain several approaches for identifying of K-fusion frames. The main purpose is to reconstruct the elements from the range of the bounded operator K on a Hilbert space $$\mathcal {H}$$ H by using a family of closed subspaces in $$\mathcal {H}$$ H . This work will be useful in some problems in sampling theory which are processed by fusion frames. For this end, we present some descriptions for duality of K-fusion frames and also resolution of the operator K to provide simple and concrete constructions of duals of K-fusion frames. Finally, we survey the robustness of K-fusion frames under some perturbations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

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

, Volume 73 (1) – Feb 24, 2018
26 pages

/lp/springer_journal/characterization-and-construction-of-k-fusion-frames-and-their-duals-o6MhSd4fiY
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-018-0781-1
Publisher site
See Article on Publisher Site

### Abstract

K-frames, a new generalization of frames, were recently considered by L. G $$\breve{\text {a}}$$ a ˘ vruţa in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a variety of applications. In the present paper, we introduce the notion of K-fusion frames in Hilbert spaces and obtain several approaches for identifying of K-fusion frames. The main purpose is to reconstruct the elements from the range of the bounded operator K on a Hilbert space $$\mathcal {H}$$ H by using a family of closed subspaces in $$\mathcal {H}$$ H . This work will be useful in some problems in sampling theory which are processed by fusion frames. For this end, we present some descriptions for duality of K-fusion frames and also resolution of the operator K to provide simple and concrete constructions of duals of K-fusion frames. Finally, we survey the robustness of K-fusion frames under some perturbations.

### Journal

Results in MathematicsSpringer Journals

Published: Feb 24, 2018

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