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

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Abstract

K-frames, a new generalization of frames, were recently considered by L. G\(\breve{\text {a}}\)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 \(\mathcal {H}\) by using a family of closed subspaces in \(\mathcal {H}\). 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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran

    Fahimeh Arabyani Neyshaburi & Ali Akbar Arefijamaal

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  1. Fahimeh Arabyani Neyshaburi
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  2. Ali Akbar Arefijamaal
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Correspondence to Fahimeh Arabyani Neyshaburi.

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Arabyani Neyshaburi, F., Arefijamaal, A.A. Characterization and Construction of K-Fusion Frames and Their Duals in Hilbert Spaces. Results Math 73, 47 (2018). https://doi.org/10.1007/s00025-018-0781-1

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  • DOI: https://doi.org/10.1007/s00025-018-0781-1

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