Abstract
K-g-frames are a generalization of g-frames that have better advantages in practical applications than g-frames. In this paper, we focus on the constructions of K-g-frames for Hilbert spaces by certain operators with specific properties, while starting with a given K-g-frame or just a g-Bessel sequence. In addition, two recent concepts about linear operators are used to construct K-g-frames, which differ from existing methods. Also, we generalize some of the known results in frame theory to K-g-frames and present some necessary conditions for K-g-frames.
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Acknowledgements
The authors would like to thank the referees for their suggestions. This work is supported by the National Natural Science Foundation of China (No. 11761001), First-class Disciplines of NingXia (No. NXYLXK2017B09), Leading Talent Project of Science and Technology Innovation of NingXia (No. KJT2016002) and Major Project of North Minzu University (No. ZDZX201801).
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Huang, Y., Shi, S. New Constructions of K-g-Frames. Results Math 73, 162 (2018). https://doi.org/10.1007/s00025-018-0924-4
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DOI: https://doi.org/10.1007/s00025-018-0924-4