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

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We prove that if two closed disks X 1 and X 2 of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then the intersection X 1\cap X 2 is a complete 2+2-\sqrt{3}-spectral set for A. When the intersection of X 1 and X 2 is an annulus, this result gives a positive answer to a question of A.L. Shields 1974.

Autor: Catalin Badea; Bernhard Beckermann; Michel Crouzeix

Fuente: https://archive.org/