Abstract
K-frames were recently introduced by Găvruţa in Hilbert spaces to study atomic systems with respect to a bounded linear operator. From her discussions there are many differences between K-frames and ordinary frames, so in this paper we further discuss the interchangeability of two Bessel sequences with respect to a K-frame, where K is a bounded linear operator with closed range. We also give several methods to construct K-frames. In the end we discuss the stability of a more general perturbation for K-frame.
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X. Xiao is partly supported by the Scientific Research Start-up Foundation of Fuzhou University, China (Grant No. 022410), the Science and Technology Funds from the Fuzhou University, China (Grant No. 2012-XQ-29), Y. Zhu is partly supported by the Natural Science Foundation of Fujian Province, China (Grant No. 2012J01005).
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Xiao, X., Zhu, Y. & Găvruţa, L. Some Properties of K-Frames in Hilbert Spaces. Results. Math. 63, 1243–1255 (2013). https://doi.org/10.1007/s00025-012-0266-6
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DOI: https://doi.org/10.1007/s00025-012-0266-6