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

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

2007-12-04

arxiv.org/abs/0712.0522v1

Mathematics

Spectral Theory

10 pages

Scientific paper

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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