A functional calculus based on the numerical range: applications

Michel Crouzeix (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We develop a functional calculus for both bounded and unbounded operators in Hilbert spaces based on a simple inequality related to polynomial functions of a square matrix and involving the numerical range. We present some applications in different areas of mathematics.

Mots clés: functional calculus; numerical range; spectral set

Domaines: Analyse numérique [math.NA]

Michel Crouzeix. A functional calculus based on the numerical range: applications. Linear and Multilinear Algebra, 2008, 56 (1-2), pp.81-103. ⟨10.1080/03081080701336610⟩. ⟨hal-00361123⟩