Some Results on Controlled K-Frames in Hilbert Spaces

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M. Nouri, A. Rahimi, SH. Najafzadeh, Some Results on Controlled K-Frames in Hilbert Spaces, Int. J. Anal. Appl., 16 (1) (2018), 62-74.

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M. Nouri, A. Rahimi, SH. Najafzadeh

Abstract

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also K-frames have been introduced to study atomic systems with respect to bounded linear operator. In this paper, the notion of controlled K-frames will be studied and it will be shown that controlled K-frames are equivalent to K-frames under some mild conditions. Finally, the stability of controlled K-Bessel sequences under perturbation will be discussed with some examples.

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