Convex domains and K-spectral sets

Catalin Badea (1) , Michel Crouzeix , Bernard Delyon (2)

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

Let $\Omega$ be an open convex domain of the complex plane. We study constants K such that $\Omega$ is K-spectral or complete K-spectral for each continuous linear Hilbert space operator with numerical range included in $\Omega$. Several approaches are discussed.

Domaines: Analyse fonctionnelle [math.FA]; Algèbres d'opérateurs [math.OA]

Catalin Badea, Michel Crouzeix, Bernard Delyon. Convex domains and K-spectral sets. Mathematische Zeitschrift, 2006, 252 (2), pp.345-365. ⟨10.1007/s00209-005-0857-y⟩. ⟨hal-00012448⟩