K-frames were recently introduced by L. Gavruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by P. Balazs in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this manuscript, we will define the concept of the controlled K-frames and will show that controlled K-frames are equivalent to K-frames and so the controlled operator C can be used as preconditions in applications.
Keywords and Phrases
Frame, Bessel sequence, Controlled frame, K-frame, Atomic system.
A.M.S. subject classiﬁcation
Primary 42C40; Secondary 41A58, 47A58.