Intersections of several disks of the Riemann sphere as K-spectral sets
By Catalin Badea, Bernhard Beckermann, Michel Crouzeix. 2008
49 citations recorded by the source corpus.
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).
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7997831ed79420560579d3fef1d8b17dd4d30efd
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- H^\infty functional calculus and square function estimates for Ritt operators (2012, background): “ for the development of various topics around functional calculus estimates on Hilbert space, including polynomial boundedness, K-spectral sets and related similarity problems. We refer the reader to [5, 48, 49, 52] and the references therein for a large information. See also [13, 11] for striking r”