A note on a spectral constant associated with an annulus

Georgios Tsikalas

paper

A note on a spectral constant associated with an annulus

arXiv:2106.00176

Abstract

Fix $R > 1$ and let $A_{R} = {1/ R \leq ∣ z ∣ \leq R}$ be an annulus. Also, let $K (R)$ denote the smallest constant such that $A_{R}$ is a $K (R)$ -spectral set for the bounded linear operator $T \in B (H)$ whenever $∣∣ T ∣∣ \leq R$ and $∣∣ T^{- 1} ∣∣ \leq R .$ We show that $K (R) \geq 2, for all R > 1.$ This improves on previous results by Badea, Beckermann and Crouzeix.

4 pages