An investigation of exponentially m-isometries within the framework of semi-Hilbert spaces

In this paper, the concept of exponentially $m$-isometry \cite{Hedayatian} on a Hilbert space is generalized when an additional semi-inner product is considered. We present a comprehensive study of the algebraic properties and characterizations of operators within this extended class. Furthermore, we explore the dynamical behavior of these operators and conclude with an analysis of their spectral properties.