Some results about the Construction of K-frames in Hilbert spaces

Abstract

K-frames were proposed by Gavruta in 2012, and then some scholars began to study its properties. In this article, we first prove a sufficient condition of obtaining K-frames from the known general frames in Hilbert spaces, as well as the relevant corollarys and examples. We also show the another characterization of the properties of K-frames. Moreover, we present a method that allows the K-frames to be built from two known K-frames, and the inference is obtained by combining this method with the K-frames properties given above. In the end, we give a inequality about tight K-frames.