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.