Essential spectral radius estimates for some composition operators on $C^k( \bar{\varOmega })$
Volume 247 / 2019
Studia Mathematica 247 (2019), 191-204
MSC: Primary 47A53; Secondary 47B33.
DOI: 10.4064/sm170920-19-3
Published online: 23 November 2018
Abstract
Let $\varOmega $ be either an open cube or a bounded $C^k$ domain in $\mathbb {R}^d$, and let $\phi $ be a $C^k$ self-map of $\varOmega $ which induces a bounded composition operator $C_\phi $ on $C^k(\bar\varOmega )$. We show how the relationship between $C_\phi $ and a more complicated operator on a simpler space can be exploited to learn about some ‘essential’ properties of $C_\phi $. This mechanism allows us to extend a recent theorem of Feinstein and Kamowitz.
