Weaving K-Frames in Hilbert Spaces

Gavruta introduced K-frames for Hilbert spaces to study atomic systems with respect to a bounded linear operator. There are many differences between K-frames and standard frames, so we study weaving properties of K-frames. Two frames {phi(i)}(i is an element of I) and {psi(i)}(i is an element of I) for a separable Hilbert space are woven if there are positive constants A <= B such that for every subset sigma subset of 1, the family {phi(i)}(i is an element of sigma) boolean OR {psi(i)}(i is an element of sigma)c is a frame for with frame bounds A, B. In this paper, we present necessary and sufficient conditions for weaving K-frames in Hilbert spaces. It is shown that woven K-frames and weakly woven K-frames are equivalent. Finally, sufficient conditions for Paley-Wiener type perturbation of weaving K-frames are given.