Mathematics > Spectral Theory
[Submitted on 4 Dec 2007]
Title:K-spectral sets and intersections of disks of the Riemann sphere
View PDFAbstract: 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).
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