Sum of $g-$frames in Hilbert $C^{\ast}-$modules
Functional Analysis
2025-02-19 v2
Abstract
In this article, we study g-frames in Hilbert -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 -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.
Keywords
Cite
@article{arxiv.2312.14319,
title = {Sum of $g-$frames in Hilbert $C^{\ast}-$modules},
author = {Abdellatif Lfounoune and Hafida Massit and Abdelilah Karara and Mohamed Rossafi},
journal= {arXiv preprint arXiv:2312.14319},
year = {2025}
}