  Recently, fusion frames and frames for operators were considered as
generalizations of frames in Hilbert spaces. In this paper, we generalize some
of the known results in frame theory to fusion frames related to a linear
bounded operator K which we call K-fusion frames. We obtain new K-fusion frames
by considering K-fusion frames with a class of bounded linear operators. We
also study the stability of K-fusion frames under small perturbations. We
further give some characterizations of atomic systems with subspace sequences.
