Some Properties of K-Frames in Hilbert Spaces

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.