Controlled G-Frames and Their G-Multipliers in Hilbert spaces

摘要

Multipliers have been recently introduced by P. Balazs as operators forBessel sequences and frames in Hilbert spaces. These are operators that combine(frame-like) analysis, a multiplication with a fixed sequence (called thesymbol) and synthesis. Weighted and controlled frames have been introduced toimprove the numerical efficiency of iterative algorithms for inverting theframe operator Also g-frames are the most popular generalization of frames thatinclude almost all of the frame extensions. In this manuscript the concept ofthe controlled g-frames will be defined and we will show that controlledg-frames are equivalent to g-frames and so the controlled operators C and C0can be used as preconditions in applications. Also the multiplier operator forthis family of operators will be introduced and some of its properties will beshown.