$G$-dual Frames in Hilbert $C^{*}$-module Spaces
Journal: Sahand Communications in Mathematical Analysis (Vol.11, No. 1)Publication Date: 2018-08-01
Authors : Fatemeh Ghobadzadeh; Abbas Najati;
Page : 65-79
Keywords : Frame; $g$-dual frame; Hilbert $C^{*}$-module;
Abstract
In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames are given. A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is not satisfied in general Hilbert $C^*$-modules.
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