A note on a spectral constant associated with an annulus

2021/06/01 by Georgios Tsikalas, Tsikalas, Georgios · 2 citations
Computer Science · Mathematics · #47A10 (Secondary) #47A25 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2106.00176

openalex publication_date 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fix R>1 and let A_R=\1/R≤ |z|≤ 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∈ B(H) whenever ||T||≤ R and ||T^-1||≤ R. We show that K(R)≥ 2, for all R>1. This improves on previous results by Badea, Beckermann and Crouzeix.

Cited by

• Spectral estimates in the quantum annulus and in the numerical annulus
• Function theory on the annulus in the dp-norm

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