Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules
In the present paper, we introduce the generalized inverse operators, which have an exciting role in operator theory. We establish Douglas' factorization theorem type for the Hilbert pro-$C^{\ast}$-module.We introduce the notion of atomic system and $K$-frame in the Hilbert pro-$C^{\ast}$-mo...
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University of Maragheh
2024-03-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_709282_b1619307a596f9e48f9f42bac1fa2ceb.pdf |
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| author | Mohamed Rossafi Roumaissae Eljazzar Ram Mohapatra |
| author_facet | Mohamed Rossafi Roumaissae Eljazzar Ram Mohapatra |
| author_sort | Mohamed Rossafi |
| collection | DOAJ |
| description | In the present paper, we introduce the generalized inverse operators, which have an exciting role in operator theory. We establish Douglas' factorization theorem type for the Hilbert pro-$C^{\ast}$-module.We introduce the notion of atomic system and $K$-frame in the Hilbert pro-$C^{\ast}$-module and study their relationship. We also demonstrate some properties of the $K$-frame by using Douglas' factorization theorem.Finally we demonstrate that the sum of two $K$-frames in a Hilbert pro-$C^{\ast}$-module with certain conditions is once again a $K$-frame. |
| format | Article |
| id | doaj-art-2e7bfc04985945beb47004710aad8e92 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-2e7bfc04985945beb47004710aad8e922025-02-11T05:24:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-03-01212254910.22130/scma.2023.2001846.1318709282Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-ModulesMohamed Rossafi0Roumaissae Eljazzar1Ram Mohapatra2LaSMA Laboratory Department of Mathematics Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Fez, Morocco.Laboratory of Partial Differential Equations, Spectral Algebra and Geometry, Department of Mathematics, Faculty Of Sciences, University of Ibn Tofail, Kenitra, Morocco.Department of Mathematics, University of Central Florida, Orlando, FL., 32816, USA.In the present paper, we introduce the generalized inverse operators, which have an exciting role in operator theory. We establish Douglas' factorization theorem type for the Hilbert pro-$C^{\ast}$-module.We introduce the notion of atomic system and $K$-frame in the Hilbert pro-$C^{\ast}$-module and study their relationship. We also demonstrate some properties of the $K$-frame by using Douglas' factorization theorem.Finally we demonstrate that the sum of two $K$-frames in a Hilbert pro-$C^{\ast}$-module with certain conditions is once again a $K$-frame.https://scma.maragheh.ac.ir/article_709282_b1619307a596f9e48f9f42bac1fa2ceb.pdfdouglas majorizationatomic systemhilbert pro-$c^{\ast}$-modules |
| spellingShingle | Mohamed Rossafi Roumaissae Eljazzar Ram Mohapatra Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules Sahand Communications in Mathematical Analysis douglas majorization atomic system hilbert pro-$c^{\ast}$-modules |
| title | Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules |
| title_full | Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules |
| title_fullStr | Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules |
| title_full_unstemmed | Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules |
| title_short | Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules |
| title_sort | douglas factorization theorem and atomic system in hilbert pro c ast modules |
| topic | douglas majorization atomic system hilbert pro-$c^{\ast}$-modules |
| url | https://scma.maragheh.ac.ir/article_709282_b1619307a596f9e48f9f42bac1fa2ceb.pdf |
| work_keys_str_mv | AT mohamedrossafi douglasfactorizationtheoremandatomicsysteminhilbertprocastmodules AT roumaissaeeljazzar douglasfactorizationtheoremandatomicsysteminhilbertprocastmodules AT rammohapatra douglasfactorizationtheoremandatomicsysteminhilbertprocastmodules |