2023/12/21 by Lfounoune, Abdellatif, Hafida Massit, Massit, Hafida +3
Mathematics · Medicine · #42C15 #46C05 #47B90 #Advanced Mathematical Physics Problems #Child Abuse and Related Trauma #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2312.14319
openalex publication_date 2023/12/21 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28
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.