Sum of g-Frames in Hilbert C∗-Modules

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DOI: https://doi.org/10.28924/2291-8639-23-2025-64
Published: Mar 17, 2025
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Abdellatif Lfounoune, Hafida Massit, Abdelilah Karara, Mohamed Rossafi, Sum of g-Frames in Hilbert C∗-Modules, Int. J. Anal. Appl., 23 (2025), 64.

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Abdellatif Lfounoune, Hafida Massit, Abdelilah Karara, Mohamed Rossafi

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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