  Controlled g-atomic subspace for a bounded linear operator is being presented
and a characterization has been given. We give an example of controlled
K-g-fusion frame. We construct a new controlled K-g-fusion frame for the
Hilbert space H ? X using the controlled K-g-fusion frames of the Hilbert
spaces H and X. Several useful resolutions of the identity operator on a
Hilbert space using the theory of controlled g-fusion frames have been
discussed. Frame operator for a pair of controlled g-fusion Bessel sequences
has been introduced.
