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Constructions of K-g-Frames and Tight K-g-Frames in Hilbert Spaces

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Abstract

In this paper, we mainly discuss the constructions of some new K-g-frames which differ from the existing methods. Meanwhile, we use the relation between a positive operator and the frame operator of a K-g-frame to yield a new K-g-frame. We also obtain a necessary and sufficient condition to generate a new K-g-frame. In addition, we correct some recent results which were obtained by Huang and Leng. In the end, we give an equivalent characterization to construct some new tight K-g-frames by two given g-Bessel sequences. Our results generalize and improve some remarkable results.

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Acknowledgements

The authors cordially thank two anonymous referees for their helpful comments and suggestions to improve our manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Fuzhou University, Fuzhou, 350116, Fujian, People’s Republic of China

    Dandan Du & Yu-Can Zhu

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  1. Dandan Du
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  2. Yu-Can Zhu
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Correspondence to Yu-Can Zhu.

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Communicated by See Keong Lee.

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The author is partly supported by the Natural Science Foundation of Fujian Province, China (Grant No. 2016J01014)

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Du, D., Zhu, YC. Constructions of K-g-Frames and Tight K-g-Frames in Hilbert Spaces. Bull. Malays. Math. Sci. Soc. 43, 4107–4122 (2020). https://doi.org/10.1007/s40840-020-00911-0

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  • DOI: https://doi.org/10.1007/s40840-020-00911-0

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