Essential norms of weighted composition operators on the space ${\cal H}^{\infty}$ of Dirichlet series

Volume 191 / 2009

Pascal Lefèvre Studia Mathematica 191 (2009), 57-66 MSC: 30B50, 46E15, 47B10, 47B33. DOI: 10.4064/sm191-1-4


We estimate the essential norm of a weighted composition operator relative to the class of Dunford–Pettis operators or the class of weakly compact operators, on the space ${\cal H}^\infty $ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.


  • Pascal LefèvreFaculté Jean Perrin
    Université d'Artois
    rue Jean Souvraz S.P. 18
    62307 Lens Cedex, France

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