# Some results on higher orders quasi-isometries

## TL;DR

This paper explores the properties of n-quasi-m-isometric operators, a generalization of m-isometric operators, on infinite complex Hilbert spaces, extending previous work and providing new insights into their characteristics.

## Contribution

It introduces new properties of n-quasi-m-isometric operators, expanding the understanding of their structure and behavior beyond prior studies.

## Key findings

- Established additional properties of n-quasi-m-isometric operators
- Extended the theory of m-isometric operators to the quasi-m setting
- Contributed to the mathematical understanding of operator classes on Hilbert spaces

## Abstract

The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as n-quasi-m-isometric operators acting on an infinite complex separable Hilbert space H. This generalizes the class of m-isometric operators on Hilbert space introduced by Agler and Stankus in [1]. The class of n-quasi-m-isometric operators was defined by S. Mecheri and T. Prasad in [18] , where they have given some of their properties. Based, mainly, on [2], [3], [5] and [9], we contribute some other properties of such operators.