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Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^ast-$modules

Journal: Sahand Communications in Mathematical Analysis (Vol.15, No. 1)

Publication Date:

Authors : ;

Page : 135-146

Keywords : Frame; $g$-frame; Fusion frame; Biorthogonal sequence; Approximate duality;

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Abstract

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.

Last modified: 2019-07-27 18:10:17