INTERSECTIONS OF SEVERAL DISKS OF THE RIEMANN SPHERE AS K-SPECTRAL SETS

Catalin Badea (1) , Bernhard Beckermann (1) , Michel Crouzeix (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 IRMAR - Institut de Recherche Mathématique de Rennes

We prove that if n closed disks D-1, D-2,...,Dn, of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then their intersection D-1 boolean AND D-2 boolean AND ... boolean AND D-n is a complete K-spectral set for A, with K <= n + n(n-1)/root 3. When n = 2 and the intersection X-1 boolean AND X-2 is an annulus, this esult gives a positive answer to a question of A.L. Shields (1974).

Mots clés: Spectral set; complete K-spectral set; intersection of spectral sets; normal dilation

Domaines: Analyse numérique [math.NA]

Catalin Badea, Bernhard Beckermann, Michel Crouzeix. INTERSECTIONS OF SEVERAL DISKS OF THE RIEMANN SPHERE AS K-SPECTRAL SETS. Communications on Pure and Applied Mathematics, 2009, 8 (1), pp.37-54. ⟨10.3934/cpaa.2009.8.37⟩. ⟨hal-00365343⟩