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arXiv · 2312.14319

Sum of $g-$frames in Hilbert $C^{\ast}-$modules

Abdellatif Lfounoune·Hafida Massit·Abdelilah Karara·Mohamed Rossafi
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Abstract

In this article, we study g-frames in Hilbert $C^*$-modules and investigate conditions under which the sum of two g-frames (or a g-frame and a g-Bessel sequence) remains a g-frame. We also address the stability of g-frames under certain perturbations and provide illustrative examples in the context of $C^*$-algebras. Our results unify and extend many of the existing theorems on g-frames, focusing on the invertibility of associated operators as a key condition for guaranteeing that sums of g-frames preserve the g-frame property.

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Abdellatif Lfounoune, Hafida Massit, Abdelilah Karara, Mohamed Rossafi. 2025-02-18. Sum of $g-$frames in Hilbert $C^{\ast}-$modules. https://arxiv.org/abs/2312.14319

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