%0 Journal Article
%T $G$-Frames Generated by Iterated Operators
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Rahmani, Morteza
%D 2023
%\ 09/01/2023
%V 20
%N 4
%P 243-260
%! $G$-Frames Generated by Iterated Operators
%K Hilbert space
%K G-Frame
%K g-Riesz basis
%K Iterated operator
%R 10.22130/scma.2023.1987650.1237
%X 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.
%U https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdf