On the Sum of K-Frames in Hilbert Spaces

摘要

In recent years, research on a special class of frames, named K-frames where K is an operator, has become significant in theory and applications. Since the finite sum of K-frames may not be a K-frame for the Hilbert space, in this paper, we discuss the sum and stability of K-frames in Hilbert spaces. First, we obtain some sufficient conditions for the finite sum of a K-frame and a Bessel sequence to be a K-frame. Then we get the K-dual of the sum of K-frames by the dual of the original K-frames. In particular, we give some new results about the operator K and the analysis operator in the discussion. Moreover, we discuss the stability of K-frames and get some conclusions.