Abstract:

In this paper, we discuss the stabilities of K-frames and tight K-frames under the operator perturbation. Firstly, we provide an equivalent characterization of the operator perturbation for a K-frame by using a bounded linear operator $T $ from ${{\cal H}_1} $ to ${{\cal H}_2} $. We also give a simple way to construct new K-frames from two existing Bessel sequences. Meanwhile, we make a discussion on the construction for K-frames from given ones. In the end, we obtain a necessary and sufficient condition to generate tight K-frames from two old Bessel sequences. Our results generalize and improve the remarkable results which had been obtained by Casazza and Christensen.

Key words: K- frame, Tight K- frame, Bessel sequence, Stability