On linear chaos in function spaces

Abstract

We show that, in $L_p(0,\infty )$ ($1\le p<\infty$), 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.

Minor edits. There is a text overlap with arXiv:2106.09682 and arXiv:2106.14872 in the Preliminaries section containing introductory information, definitions, and general remarks