Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos 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 C' 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.
 A. Aldroubi, C. Cabrelli, U. Molter, Wavelets on irregular grids with arbitrary dilation matrices and frame atomics for L2 (Rd), Appl. Comput. Harmon. Anal. 17 (2004) 119-140.
 M. L. Arias, M. Pacheco, Bessel fusion multipliers, J. Math. Anal. Appl. 348(2) (2008), 581-588.
 P. Balazs, Basic definition and properties of Bessel multipliers, J. Math. Anal. Appl. 325(1) (2007) 571-585.
 P. Balazs, J.P. Antoine, A. Grybos, Wighted and Controlled Frames, Int. J. Wavelets Multiresolut. Inf. Process. 8(1) (2010) 109-132.
 P. Balazs, W.A. Deutsch, A. Noll, J. Rennison, J. White, STx Programmer Guide, Version: 3.6.2. Acoustics Research Institute, Austrian Academy of Sciences, 2005.
 P. Balazs, B. Laback, G. Eckel, W.A. Deutsch, Introducing time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking. IEEE Transactions on Audio, Speech and Language Processing, forthcoming:-, 2009.
 I. Bogdanova, P. Vandergheynst, J.P. Antoine, L. Jacques, M. Morvidone, Stereographic wavelet frames on the sphere, Applied Comput. Harmon. Anal. (19) (2005) 223-252.
 P.G. Casazza, G. Kutyniok, Frames of Subspaces, Wavelets, Frames and Operator Theory, Amer. Math. Soc. 345 (2004) 87-113.
 O. Christensen, Y.C. Eldar, Oblique dual frames and shift-invariant spaces, Appl. Comput. Harmon. Anal. 17 (2004) 48-68.
 Ph. Depalle, R. Kronland-Martinet, B. Torresani, Time-frequency multipliers for sound synthesis. In Proceedings of the Wavelet XII conference, SPIE annual Symposium, San Diego, August 2007.
 M. Dörfler, B. Torresani, Representation of operators in the time- frequency domain and generalized gabor multipliers. J. Fourier Anal. Appl. (2009).
 M. Dorfler, Gabor analysis for a class of signals called music, Ph.D. thesis, University of Vienna, 2003.
 Y.C. Eldar, Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors, J. Fourier Anal. Appl. 9 (2003) 77-96.
 H.G. Feichtinger, K. Nowak, A first survey of Gabor multipliers, Birkhauser, Boston, 2003, Chapter 5, 99-128.
 A. Fereydooni, A. Safapour, Banach pair frames.
 A. Fereydooni, A. Safapour, Pair frames, arXiv:1109.3766v2.
 A. Fereydooni, A. Safapour, A. Rahimi, Aadjoint of pair frames, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys 2013.
 M. Fornasier, Decomposition of Hilbert spaces: local construction of global frames, Proc. Int. Conf. on Constructive function theory, Varna, B. Bo- janov Ed., DARBA, Sofia, 2003 275-281.
 M. Fornasier, Quasi-orthogonal decompsition of structured frames, J. Math. Anal. Appl. 289 (2004) p 180-199.
 H. Heuser, Functional analysis, John Wiley, New York, 1982.
 S. Li, H. Ogawa, Pseudoframes for subspaces with application, J. Fourier Anal. Appl. 10 (2004) 409-431.
 G. Matz, F. Hlawatsch, Linear Time-Frequency Filters: On-line Algorithms and Applications, chapter 6 in ’Application in Time-Frequency Signal Processing’, pp. 205-271. eds. A. Papandreou-Suppappola, Boca Raton (FL): CRC Press, 2002.
 G. Matz, D. Schafhuber, K. Grochenig, M. Hartmann, F. Hlawatsch, Analysis, Optimization, and Implementation of Low-Interference Wireless Multicarrier Systems. IEEE Trans. Wireless Comm. 6(4) (2007) 111.
 A. Najati, , M.H. Faroughi, A. Rahimi, G-frames and stability of g-frames in Hilbert spaces, Methods Funct. Anal. Topology. 14 (2008) 271-286.
 A. Najati, A. Rahimi, Generalized Frames in Hilbert spaces, Bull. Iranian Math. Soc. 35(1) (2009) 97-109.
 P. Oswald, Multilevel Finite Element Approximation: Theory and Application, Teubner Skripten zur Numerik, Teubner, Stuttgart, 1994.
 A. Rahimi, Frames and Their Generalizations in Hilbert and Banach Spaces, LAP Lambert Academic Publishing, 2011.
 A. Rahimi, Multipliers of Genralized frames in Hilbert spaces, Bull. Iranian Math. Soc. 37(1) (2011) 63-88.
 A. Rahimi, P. Balazs, Multipliers of p-Bessel sequences in Banach spaces, Integral Equations Operator Theory, 68(2) (2010) 193-205.
 R. Schatten, Norm Ideals of Completely Continious Operators, Springer, Berlin, 1960.
 W. Sun, G-frames and G-Riesz bases, J. Math. Anal. Appl. 322(1) (2006) 437-452.
 K. Zhuo, Operator Theory in Function Spaces, Marcel Dekker, Inc, 1990.