On composition operators on the Wiener algebra of Dirichlet series

Daniel Li (1, 2) , Hervé Queffélec (3, 4) , Luis Rodríguez-Piazza (5, 6)

1 LML - Laboratoire de Mathématiques de Lens
2 UA - Université d'Artois
3 Université de Lille
4 LPP - Laboratoire Paul Painlevé
5 Departamento de Analisis Matematico
6 Universidad de Sevilla / University of Sevilla

We show that the symbol of a bounded composition operator on the Wiener algebra of Dirichlet series does not need to belong to this algebra. Our example even gives an absolutely summing (hence compact) composition operator.

Keywords: MSC 2010 primary: 47B33 secondary: 30B50 Key-words Composition operator Dirichlet series; MSC 2010 primary: 47B33; secondary: 30B50 Key-words Composition operator; Dirichlet series

Domains: Functional Analysis [math.FA]

Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. On composition operators on the Wiener algebra of Dirichlet series. 2022. ⟨hal-03894276⟩