Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules
In the present article, duals, approximate duals and pseudo-duals (generated by bounded and not necessarily adjointable operators) of a frame in a Hilbert $C^\ast$-module are characterized and some of their properties are obtained. Especially, the ones constructed by multiplication operators are dis...
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University of Maragheh
2024-10-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_715725_a5db7c1621d33e6b1f50c9cad1e1f44a.pdf |
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| author | Morteza Mirzaee Azandaryani |
| author_facet | Morteza Mirzaee Azandaryani |
| author_sort | Morteza Mirzaee Azandaryani |
| collection | DOAJ |
| description | In the present article, duals, approximate duals and pseudo-duals (generated by bounded and not necessarily adjointable operators) of a frame in a Hilbert $C^\ast$-module are characterized and some of their properties are obtained. Especially, the ones constructed by multiplication operators are discussed and their stability under the action of morphisms is focused and some equivalent conditions for the stability are derived. Finally, we get some results on pseudo-duals of modular Riesz bases, mainly their preservation under the action of morphisms and their behavior in the presence of semi-normalized symbols are studied. |
| format | Article |
| id | doaj-art-dd2570aa66244764bbc6ee71cbc6d628 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-dd2570aa66244764bbc6ee71cbc6d6282025-02-11T05:27:48ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-10-0121417318910.22130/scma.2024.2022517.1611715725Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-ModulesMorteza Mirzaee Azandaryani0Department of Mathematics, University of Qom, Qom, Iran.In the present article, duals, approximate duals and pseudo-duals (generated by bounded and not necessarily adjointable operators) of a frame in a Hilbert $C^\ast$-module are characterized and some of their properties are obtained. Especially, the ones constructed by multiplication operators are discussed and their stability under the action of morphisms is focused and some equivalent conditions for the stability are derived. Finally, we get some results on pseudo-duals of modular Riesz bases, mainly their preservation under the action of morphisms and their behavior in the presence of semi-normalized symbols are studied.https://scma.maragheh.ac.ir/article_715725_a5db7c1621d33e6b1f50c9cad1e1f44a.pdfhilbert c*-moduleframedualapproximate dualpseudo-dualmodular riesz basis |
| spellingShingle | Morteza Mirzaee Azandaryani Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules Sahand Communications in Mathematical Analysis hilbert c*-module frame dual approximate dual pseudo-dual modular riesz basis |
| title | Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules |
| title_full | Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules |
| title_fullStr | Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules |
| title_full_unstemmed | Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules |
| title_short | Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules |
| title_sort | pseudo duals of frames and modular riesz bases in hilbert c ast modules |
| topic | hilbert c*-module frame dual approximate dual pseudo-dual modular riesz basis |
| url | https://scma.maragheh.ac.ir/article_715725_a5db7c1621d33e6b1f50c9cad1e1f44a.pdf |
| work_keys_str_mv | AT mortezamirzaeeazandaryani pseudodualsofframesandmodularrieszbasesinhilbertcastmodules |