On linear chaos in function spaces

TL;DR

This paper demonstrates that certain weighted translation operators in various function spaces exhibit chaotic behavior, extending known results and analyzing their spectral properties.

Contribution

It establishes chaos for bounded and unbounded weighted translation operators in multiple function spaces, extending previous work and characterizing their spectra.

Findings

Weighted translations are chaotic in $L_{p}(0, olinebreak \infty)$ for $1 olinebreak \leq p < olinebreak \infty$.

Unbounded weighted translations are also chaotic in these spaces and in $C_{0}[0, olinebreak \infty)$.

Spectral descriptions are provided for complex spaces.

Abstract

We show that, in $L_{p}(0,\infty)$ ($1\leq p <\infty$), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to $C_{0}[0,\infty)$ and describe the spectra of the weighted translations provided the underlying spaces are complex.