Tight frames are similar to orthogonal bases, except that the frame coefficients are not unique, but they are stable in calculations and numerical algorithms. Not all frames are tight frames, but some have the ability to become tight frames. These frames are called scalable frames. In this article, we extend this good property of frames to G-frames. For this purpose, we define the scalable G-frame based on the diagonal operators, and obtain a preconditioner for its analysis operator by block diagonal operator. We also provide the necessary and sufficient conditions for the scalability of the G-frames based on the frames induced by the G-frames.
