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arXiv · 2106.00176

A note on a spectral constant associated with an annulus

Georgios Tsikalas
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Abstract

Fix $R>1$ and let $A_R=\{1/R\le |z|\le R \}$ 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 $T\in \mathcal{B}(H)$ whenever $||T||\le R$ and $||T^{-1}||\le R.$ We show that $K(R)\ge 2, \text{ for all } R>1. $ This improves on previous results by Badea, Beckermann and Crouzeix.

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Georgios Tsikalas. 2021-06-01. A note on a spectral constant associated with an annulus. https://arxiv.org/abs/2106.00176

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