Mostafa Mbekhta (Université de Lille) : Conorme locale d'un opérateur dans un espace de Hilbert

Orateur : Mostafa Mbekhta

Affiliation : Université de Lille

Date : 16 Septembre 2022

Heure : 14h

Lieu : Salle Kampé de Fériet, Bâtiment M2 

Résumé : Let H be a complex Hilbert space and let B(H) be the algebra of all bounded linear operators on H. In this talk, for T ∈B(H) and a unit vector x ∈ H, we introduce a local version of the conorm (reduced minimum modulus) of T at x, noted by γ(T, x). Properties of this quantity are investigated. We study the relations between γ(T, x) and the Moore-Penrose inverse, spectrum of T and the local spectrum of T at x. At the end of this talk we will be interested in several problems around this quantity (preserving, continuity, local spectral theory).