Strongly $n$-supercyclic operators

TL;DR

This paper explores the properties of strongly n-supercyclic operators, a recently introduced class that is stronger than n-supercyclicity, revealing their spectral characteristics and providing illustrative examples and counterexamples.

Contribution

The paper establishes spectral properties of strongly n-supercyclic operators and offers new examples and counterexamples addressing open questions.

Findings

Strongly n-supercyclic operators have distinctive spectral features.

Examples demonstrate the existence of such operators.

Counterexamples clarify the boundaries of their properties.

Abstract

In this paper, we are interested in the properties of a new class of operators, recently introduced by Shkarin, called strongly $n$-supercyclic operators. This notion is stronger than $n$-supercyclicity. We prove that such operators have interesting spectral properties and give examples and counter-examples answering some natural questions asked by Shkarin.