Some Properties of Continuous K-frames in Hilbert Spaces

The theory of continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory. The K-frames were introduced by Gavruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of K-frames, there are many differences between K-frames and standard frames. K-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous K-frames or briefly cK-frames, namely some operators preserving and some identities for cK-frames. Also, the stability of these frames are discussed.