A note on a spectral constant associated with an annulus

Abstract

We introduce and study a scale of operator classes on the annulus that is motivated by the Cρ classes of ρ-contractions of Nagy and Foiaş. In particular, our classes are defined in terms of the contractivity of the double-layer potential integral operator over the annulus. We prove that if, in addition, complete contractivity is assumed, then one obtains a complete characterization involving certain variants of the Cρ classes. Recent work of Crouzeix-Greenbaum and Schwenninger-de Vries allows us to also obtain relevant K-spectral estimates, generalizing existing results from the literature on the annulus. Finally, we exhibit a special case where these estimates can be significantly strengthened.

Geometric Dilations and Operator Annuli

“…See Section 2. Later in this introduction we discuss connections between the quantum annulus and other operator annuli [BY+,CG,Ts+,Ts22].…”