Generalized essential norm of weighted composition operators on some uniform algebras of analytic functions.

Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis opertors or weakly compact operators, on some uniform algebras of analytic functions. Even in the frame of $H^\infty$ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence of a general study of weighted composition operators.

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre. Generalized essential norm of weighted composition operators on some uniform algebras of analytic functions.. Integral Equations and Operator Theory, 2009, 63, pp.557-569. ⟨hal-00859025⟩