Intersections of several disks of the Riemann sphere as K-spectral sets

Catalin Badea; Bernhard Beckermann; Michel Crouzeix

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arXiv · 0807.3136

Intersections of several disks of the Riemann sphere as K-spectral sets

Catalin Badea·Bernhard Beckermann·Michel Crouzeix

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Abstract

We prove that if $n$ closed disks $D_1, D_2, ..., D_n$, of the Riemann sphere are spectral sets for a bounded linear operator $A$ on a Hilbert space, then their intersection $D_1\cap D_2...\cap D_n$ is a complete $K$-spectral set for $A$, with $K\leq n+n(n-1)/\sqrt3$. When $n=2$ and the intersection $X_1\cap X_2$ is an annulus, this result gives a positive answer to a question of A.L. Shields (1974).

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BibTeX RIS

Catalin Badea, Bernhard Beckermann, Michel Crouzeix. 2008-07-21. Intersections of several disks of the Riemann sphere as K-spectral sets. https://arxiv.org/abs/0807.3136

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