$G$-Frames Generated by Iterated Operators
Assuming that $\Lambda$ is a bounded operator on a Hilbert space $H$, this study investigate the structure of the $g$-frames generated by iterations of $\Lambda$. Specifically, we provide characterizations of $g$-frames in the form of $\{\Lambda^n\}_{n=1}^{\infty}$ and describe some conditions un...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2023-09-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdf |
| _version_ | 1797666561565130752 |
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| author | Morteza Rahmani |
| author_facet | Morteza Rahmani |
| author_sort | Morteza Rahmani |
| collection | DOAJ |
| description | Assuming that $\Lambda$ is a bounded operator on a Hilbert space $H$, this study investigate the structure of the $g$-frames generated by iterations of $\Lambda$. Specifically, we provide characterizations of $g$-frames in the form of $\{\Lambda^n\}_{n=1}^{\infty}$ and describe some conditions under which the sequence $\{\Lambda^n\}_{n=1}^{\infty}$ forms a $g$-frame for $H$. Additionally, we verify the properties of the operator $\Lambda$ when $\{\Lambda^n\}_{n=1}^{\infty}$ is a $g$-frame for $H$. Moreover, we study the $g$-Riesz bases and dual $g$-frames which are generated by iterations. Finally, we discuss the stability of these types of $g$-frames under some perturbations. |
| first_indexed | 2024-03-11T20:00:10Z |
| format | Article |
| id | doaj.art-268e4f0698d149938d5a5629ff37fdba |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-03-11T20:00:10Z |
| publishDate | 2023-09-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-268e4f0698d149938d5a5629ff37fdba2023-10-04T08:29:39ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002023-09-0120424326010.22130/scma.2023.1987650.1237705803$G$-Frames Generated by Iterated OperatorsMorteza Rahmani0Young Researchers and Elite Club, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran.Assuming that $\Lambda$ is a bounded operator on a Hilbert space $H$, this study investigate the structure of the $g$-frames generated by iterations of $\Lambda$. Specifically, we provide characterizations of $g$-frames in the form of $\{\Lambda^n\}_{n=1}^{\infty}$ and describe some conditions under which the sequence $\{\Lambda^n\}_{n=1}^{\infty}$ forms a $g$-frame for $H$. Additionally, we verify the properties of the operator $\Lambda$ when $\{\Lambda^n\}_{n=1}^{\infty}$ is a $g$-frame for $H$. Moreover, we study the $g$-Riesz bases and dual $g$-frames which are generated by iterations. Finally, we discuss the stability of these types of $g$-frames under some perturbations.https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdfhilbert spaceg-frameg-riesz basisiterated operator |
| spellingShingle | Morteza Rahmani $G$-Frames Generated by Iterated Operators Sahand Communications in Mathematical Analysis hilbert space g-frame g-riesz basis iterated operator |
| title | $G$-Frames Generated by Iterated Operators |
| title_full | $G$-Frames Generated by Iterated Operators |
| title_fullStr | $G$-Frames Generated by Iterated Operators |
| title_full_unstemmed | $G$-Frames Generated by Iterated Operators |
| title_short | $G$-Frames Generated by Iterated Operators |
| title_sort | g frames generated by iterated operators |
| topic | hilbert space g-frame g-riesz basis iterated operator |
| url | https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdf |
| work_keys_str_mv | AT mortezarahmani gframesgeneratedbyiteratedoperators |