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

الأصل · EN

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).