Weighted and Controlled Continuous g-Frames and their Multipliers in Hilbert Spaces

Abstract

A generalization of weighted, multiplier, controlled from frame and Bessel sequences to continuous g-frames and continuous g-Bessel sequences in Hilbert spaces is presented in this study. Moreover, we find a dual of a continuous g-frame in the case that the multiplier operator is invertible. Finally, it is demonstrated that a controlled continuous g-frame is equivalent to a continuous g-frame.