G-frames in Hilbert Modules Over Pro-C*-algebras
نویسنده: Haddadzadeh، N؛
Autumn 2017, Volume 9 - Number 4 (9 صفحه - از 259 تا 267)
G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coecients. 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.
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