Ideal of hypercyclic operators that factor through $\ell^p$

TL;DR

This paper investigates the properties of hypercyclic backward weighted shift operators that factor through l^p, focusing on their injective and surjective hulls within operator ideals.

Contribution

It introduces a detailed analysis of hypercyclic operators factoring through l^p and characterizes their injective and surjective hulls, advancing understanding of their structure.

Findings

Characterization of injective and surjective hulls of these operator ideals

Identification of conditions for hypercyclicity in weighted shifts

Insights into the structure of operators factoring through l^p

Abstract

We study the injective and surjective hull of operator ideals generated by hypercyclic backward weighted shifts that factor through $\ell^p$.