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)(infinity) and describe some conditions under which the sequence {Lambda(n)}(n=1)(infinity) forms a g-frame for H. Additionally, we verify the properties of the operator Lambda when {Lambda(n)}(n=1)(infinity) 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.