  Frames for operators or k-frames were recently considered by Gavruta (2012)
in connection with atomic systems. Also generalized frames are important frames
in the Hilbert space of bounded linear operators. Fusion frames, which are a
special case of generalized frames have various applications. This paper
introduces the concept of generalized fusion frames for operators aka
k-g-fusion frames and we get some results for characterization of these frames.
We further discuss on duals and Q-duals in connection with k-g-fusion frames.
Also we obtain some useful identities for these frames. We also give several
methods to construct k-g-fusion frames. The results of this paper can be used
in sampling theory which are developed by g-frames and especially fusion
frames. In the end, we discuss the stability of a more general perturbation for
k-g-fusion frames.
