G-frames in Hilbert Modules Over Pro-C*-‎algebras

Document Type : Research Paper


Department of Mathematics, Abadan Branch, Islamic Azad University, Abadan, ‎Iran.


G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first 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.‎