Structure and applications of n-quasi exponentially m-isometric operators

In this paper, we aim to extend the established theory of exponentially m-isometric operators by introducing and exploring the concept of n-quasi-exponentially m-isometric operators. This generalization allows us to investigate a broader class of operators. We provide a comprehensive analysis of various key properties of these operators, which are illustrated through specific matrix representations. An examination of their spectral properties is also provided. The open questions presented at the end pave the way for further research and the continued advancement of the theory of m-isometries and related operators.