Some Characterizations And The Perturbations Of K-frames

In this paper we discuss the K-frames in infinite dimensional Hilbert spaces. We study the characterizations of relative operators based on the properties of K-frames. We present that a Bessel sequence can be a K-frame when it is acted on by K and K*. Also, we discuss the perturbations of K-frames with one coefficient and three coefficients and then obtain some generalized results of exact K-frames. At last, we research the perturbation of l2-linearly independent K-frames based on exact K-frames.