Sum of $g-$frames in Hilbert $C^{\ast}-$modules
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912234563698688 |
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| author | Lfounoune, Abdellatif Massit, Hafida Karara, Abdelilah Rossafi, Mohamed |
| author_facet | Lfounoune, Abdellatif Massit, Hafida Karara, Abdelilah Rossafi, Mohamed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14319 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sum of $g-$frames in Hilbert $C^{\ast}-$modules Lfounoune, Abdellatif Massit, Hafida Karara, Abdelilah Rossafi, Mohamed Functional Analysis 42C15, 46C05, 47B90 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. |
| title | Sum of $g-$frames in Hilbert $C^{\ast}-$modules |
| topic | Functional Analysis 42C15, 46C05, 47B90 |
| url | https://arxiv.org/abs/2312.14319 |