G-FRAMES IN HILBERT PRO-C*-MODULES

Abstract

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames which provide more choices on analyzing func- tions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first gen- eralize 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 canoni- cal dual g-frames and provide a reconstruction formula for the elements of such Hilbert modules.