$G$-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 |
| Summary: | 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. |
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| ISSN: | 2322-5807 2423-3900 |