G-Frames in Hilbert Modules Over Pro-C*-‎Algebras

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. first, they were de ned in hilbert spaces and then generalized on c*-hilbert modules. in this paper, we rst generalize the concept of g-frames to hilbert modules over pro-c*-algebras. then, we introduce the g-frame operators in such spaces and show that they share many useful properties with their corresponding notions in hilbert spaces. we also show that, by having a g-frame and an invertible operator in this spaces, we can produce the corresponding dual g-frame. finally we introduce the canonical dual g-frames and provide a reconstruction formula for the elements of such hilbert modules.