Polynomially quasi-(A,m)-isometric operators on a Hilbert space

Abstract

This paper aims to generalize the class of linear bounded operators on Hilbert spaces, introducing the notion of polynomially quasi-(A,m)-isometric operators. This class unifies the properties of n-quasi-(A,m)-isometric operators and polynomially quasi-m-isometric operators. We define this new class, provide a detailed characterization, and develop its matrix representation. Furthermore, we investigate the spectral properties of these operators. Our results are motivated by [M.O.A Sid Ahmed,  Ahmad, N. Note on polynomially quasi-m-isometric hilbert space operators. J Anal (2024).$ https://doi.org/10.1007/s41478-024-00847-9$].