K-spectral sets and intersections of disks of the Riemann sphere

2007/12/04 by Cătălin Badea, Catalin Badea, Badea, Catalin +4
Mathematics · #47A25 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:47A25

paper · pdf · doi:10.48550/arxiv.0712.0522

10 pages

arxiv created 2007/12/04 · openalex publication_date 2007/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if two closed disks X₁ and X₂ of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then the intersection X₁∩ X₂ is a complete (2+2/√(3))-spectral set for A. When the intersection of X₁ and X₂ is an annulus, this result gives a positive answer to a question of A.L. Shields (1974).

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