$G$-dual Frames in Hilbert $C^{*}$-module Spaces

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.

Keywords

• Frame
• $g$-dual frame
• Hilbert $C^{*}$-module