Absolutely summing weighted composition operators on Bloch spaces

Pascal Lefèvre (1) , Tonie Fares (1)

1 LML - Laboratoire de Mathématiques de Lens

We characterize p-summing composition operators C ϕ (f) = f • ϕ from a Bloch space B µ to another such space B β , where µ, β > 0. The corresponding result on little Bloch-type spaces is also proved. In addition, we construct an example of a conformal mapping of the unit disk D into itself which has a contact point with the unit circle T, and induces a compact composition operator, that fails to be p-summing for any p ≥ 1. We also detail the case of lens maps. Moreover we explore the case of weighted composition operators uC ϕ (f) = u.(f • ϕ) and characterize such nuclear operators, and p-summing ones for a class of weights. We also show that compactness of a composition operator on B β and B β 0 implies its compactness on Bergman spaces. Moreover when β > 1 the converse is also true for composition operators on B β 0 .

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre, Tonie Fares. Absolutely summing weighted composition operators on Bloch spaces. 2022. ⟨hal-03579222⟩