MULTIPLIERS OF CONTROLLED GENERALIZED FRAMES IN HILBERT SPACES

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern the symbol), which is inserted between the analysis and synthesis operators [1, 2, 3]. Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator [4]. Also, g-frames are the recent generalization of frames that include almost all of the frame extensions. In this paper, the concept of the controlled g-frames will be defined, and the multiplier operator for this family of operators will be introduced. Moreover, some of its properties will be shown