Rolewicz-type chaotic operators

TL;DR

This paper introduces a new class of Rolewicz-type operators in l_p spaces, demonstrating their chaotic behavior and stability under large linear combinations, expanding understanding of chaos in linear operators.

Contribution

It presents a novel class of chaotic Rolewicz-type operators in l_p spaces and shows their robustness under linear combinations, with a continuum of such operators.

Findings

Existence of a continuum of chaotic Rolewicz-type operators in l_p.

Chaotic property persists under large linear combinations.

A countable collection of operators with all finite linear combinations chaotic.

Abstract

In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.