A Class of n-Tuples with Finite Ascent and Peturbations

TL;DR

This paper investigates the stability of the ascent property of mutually commuting n-tuples of operators under perturbations, generalizing existing results and introducing a new class of n-tuples with stable ascent characteristics.

Contribution

It introduces a new class of n-tuples that maintain ascent stability under perturbations and generalizes known operator results to n-tuple settings.

Findings

Established stability conditions for the ascent of n-tuples under perturbations

Generalized classical operator ascent results to n-tuple contexts

Identified a new class of n-tuples with stable ascent properties

Abstract

In this paper, we are interested to study the stability of the ascent of a mutually commuting n-tuple T submitted to a perturbation by an n-tuple S which commutes mutually with T. This study lead us to generalize some well known results for operators and introduce a class of n-tuples in which we obtain the stability of the ascent of T.