Abstract
In this paper we mainly study the stabilities of K-frames under the operator perturbation. Firstly, we provide several sufficient conditions of the operator perturbation for a K-frame by using a bounded linear operator T from \({H_1}\) to \({H_2}\). We also give an equivalent characterization of the operator perturbation for a tight K-frame. Meanwhile, we correct two results which were obtained by Ramu. Lastly, we show that a K-frame can construct a T-frame by the perturbation of a bounded linear operator T. Our results generalize the remarkable results of the operator perturbation for a frame which were obtained by Casazza, Christensen, etc. when we take \(K = I\).
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The work is partly supported by the Natural Science Foundation of Fujian Province, China (Grant No. 2016J01014)
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Jia, M., Zhu, YC. Some Results About the Operator Perturbation of a K-Frame. Results Math 73, 138 (2018). https://doi.org/10.1007/s00025-018-0902-x
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DOI: https://doi.org/10.1007/s00025-018-0902-x