  k-frames were recently introduced by Gavruta in Hilbert spaces to study
atomic systems with respect to a bounded linear operator. A continuous frame is
a family of vectors in Hilbert space which allows reproductions of arbitrary
elements by continuous super positions. We construct a continuous k-frame, so
called ck-frame along with an atomic system for this version of frames. Also we
introduce a new method for obtaining the dual of a ck-frame and we prove some
new results about it.
