On the chaoticity of derivatives

TL;DR

This paper proves that derivatives exhibit chaotic behavior in certain function spaces using a new sufficient condition for linear chaos.

Contribution

It introduces a novel sufficient condition for linear chaos and applies it to demonstrate the chaoticity of derivatives in specific function spaces.

Findings

Derivatives are chaotic in $C[a,b]$ and $L_p(a,b)$ spaces.

A new sufficient condition for linear chaos is established.

Chaoticity of derivatives is proven using this condition.

Abstract

We utilize a recently established by the author sufficient condition for linear chaos to prove the chaoticity of derivatives in the spaces $C[a,b]$ and $L_p(a,b)$ ($-\infty<a<b<\infty$, $1\le p<\infty$).