G-Frames Generated by Iterated Operators

Assuming that Λ is a bounded operator on a Hilbert space H, this study investigate the structure of the g-frames generated by iterations of Λ. Specifically, we provide characterizations of g-frames in the form of {Λn}∞ n=1 and describe some conditions under which the sequence {Λn}∞ n=1 forms a g-frame for H. Additionally, we verify the properties of the operator Λ when {Λn}∞ n=1 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..