@article {
author = {Rahmani, Morteza},
title = {$G$-Frames Generated by Iterated Operators},
journal = {Sahand Communications in Mathematical Analysis},
volume = {20},
number = {4},
pages = {243-260},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.1987650.1237},
abstract = {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.},
keywords = {Hilbert space,G-Frame,g-Riesz basis,Iterated operator},
url = {https://scma.maragheh.ac.ir/article_705803.html},
eprint = {https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdf}
}