TY - JOUR
ID - 705803
TI - $G$-Frames Generated by Iterated Operators
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Rahmani, Morteza
AD - Young Researchers and Elite Club, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran.
Y1 - 2023
PY - 2023
VL - 20
IS - 4
SP - 243
EP - 260
KW - Hilbert space
KW - G-Frame
KW - g-Riesz basis
KW - Iterated operator
DO - 10.22130/scma.2023.1987650.1237
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_705803.html
L1 - https://scma.maragheh.ac.ir/article_705803_2c9e64d7597d2e9ed45cb9e120b0800e.pdf
ER -