  Multipliers have been recently introduced by P. Balazs as operators for
Bessel sequences and frames in Hilbert spaces. These are operators that combine
(frame-like) analysis, a multiplication with a fixed sequence (called the
symbol) and synthesis. Weighted and controlled frames have been introduced to
improve the numerical efficiency of iterative algorithms for inverting the
frame operator Also g-frames are the most popular generalization of frames that
include almost all of the frame extensions. In this manuscript the concept of
the controlled g-frames will be defined and we will show that controlled
g-frames are equivalent to g-frames and so the controlled operators C and C0
can be used as preconditions in applications. Also the multiplier operator for
this family of operators will be introduced and some of its properties will be
shown.
