K-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a linear and bounded operator in a Hilbert space.In this paper, we first make a discussion on relations between K-frames and frames.We obtain that a tight K-frame turns to be a frame if and only if the linear and bounded operator K is surjective, and then give a necessary and sufficient condition for a K-frame with closed range operator K.We also study the constructions of K-frames under some conditions.Finally we study the stabilities of K-frames under small perturbations.
Ming Ling DING, Xiang Chun XIAO, Yu Can ZHU. K-Frames in Hilbert Spaces. Acta Mathematica Sinica, Chinese Series, 2014, 57(6): 1089-1100 https://doi.org/10.12386/A2014sxxb0100
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