Controlled K-Fusion Frame for Hilbert Spaces

-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled -fusion frames, and we develop some results on the controlled -fusion frames for Hilbert spaces, which generalize some well known results of controlled fusion frame case. Also we discuss some characterizations of controlled Bessel -fusion sequences and of controlled -fusion frames. Further, we analyze stability conditions of controlled -fusion frames under perturbation.