On linear chaos in function spaces

John M. Jimenez, Marat V. Markin

Published 2019-12-07Version 1

We show that, in $L_{p}(0,\infty)$ $(1\leq p <\infty)$, the bounded weighted backward shift operator $(Tx)(t)=wx(t+a)$ ($w>1$ and $a>0$) and its unbounded counterpart $(Tx)(t)=w^{t}x(t+a)$ are chaotic. We also extend the unbounded case to the space $C_{0}[0,\infty)$ and analyze the spectral structure of the above operators provided the corresponding spaces are complex.