Essential norms of Volterra and Cesàro operators on Müntz spaces

Ihab Al Alam (1) , Georges Habib (1) , Pascal Lefèvre (2) , Fares Maalouf (3)

1 UNIVERSITE LIBANAISE Faculté de Sciences II
2 LML - Laboratoire de Mathématiques de Lens
3 USJ - Université Saint-Joseph de Beyrouth

We study the properties of the Volterra and Cesàro operators viewed on the L 1-Müntz space with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far from being (weakly) compact they are by computing their (generalized) essential norm. It turns out that this latter does not depend on Λ and is equal to 1/2.

Mots clés: Müntz spaces; essential norm; Volterra operator; Cesàro operator; compact operator

Domaines: Analyse fonctionnelle [math.FA]

Ihab Al Alam, Georges Habib, Pascal Lefèvre, Fares Maalouf. Essential norms of Volterra and Cesàro operators on Müntz spaces. 2016. ⟨hal-01335476v2⟩