# Classes of operators related to m-isometric operators

## TL;DR

This paper explores properties of n-quasi-(m;C)-isometric operators, demonstrating their stability under powers and products, contributing to the understanding of operator classes related to isometries.

## Contribution

It introduces and analyzes properties of n-quasi-(m;C)-isometric operators, expanding the theoretical framework of operator classes related to isometries.

## Key findings

- A power of an n-quasi-(m;C)-isometric operator remains in the same class.
- Certain products of n-quasi-(m;C)-isometric operators preserve the class.
- The paper provides foundational properties for these operator classes.

## Abstract

Isometries played a pivotal role in the development of operator theory, in particular with the theory of contractions and polar decompositions and has been widely studied due to its fundamental importance in the theory of stochastic processes, the intrinsic problem of modeling the general contractive operator via its isometric dilation and many other areas in applied mathematics. In this paper we present some properties of n-quasi-(m;C)-isometric operators. We show that a power of a n-quasi-(m;C)-isometric operator is again a n-quasi-(m;C)-isometric operator and some products and tens