Controlled g-frames in Hilbert C*-modules

The controlled frame was introduced in ۲۰۱۰ by Balazs et al. [۲], with the aim to improve the efficiency of the iterative algorithms constructed for inverting the frame operator. In this paper, the concept of controlled g-frames is introduced in Hilbert C*-modules. The equivalent condition for a controlled g-frame is established using the operator theoretic approach. Some characterizations of controlled g-frames and controlled g-Bessel sequences are found out. Moreover, the relationship between g-frames and controlled g-frames are established. In the end, some perturbation results on controlled g-frames are proved.

Keywords:

Frame , g-frame , Hilbert C*-module