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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.
Results in Mathematics – Springer Journals
Published: Feb 24, 2018
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