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Essential norms of Volterra and Cesàro operators on Müntz spaces

Volume 151 / 2018

Ihab Al Alam, Georges Habib, Pascal Lefèvre, Fares Maalouf Colloquium Mathematicum 151 (2018), 157-169 MSC: 47B07, 47B38, 30H99. DOI: 10.4064/cm7100-1-2017 Published online: 6 November 2017

Abstract

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

Authors

  • Ihab Al AlamDepartment of Mathematics
    Faculty of Sciences II
    Lebanese University
    P.O. Box 90656
    Fanar-Matn, Lebanon
    e-mail
  • Georges HabibDepartment of Mathematics
    Faculty of Sciences II
    Lebanese University
    P.O. Box 90656
    Fanar-Matn, Lebanon
    e-mail
  • Pascal LefèvreLaboratoire de Mathématiques de Lens (LML), EA 2462
    Fédération CNRS Nord-Pas-de-Calais FR 2956
    Université d’Artois
    rue Jean Souvraz S.P. 18
    62307 Lens Cedex, France
    e-mail
  • Fares MaaloufCampus des Sciences et Technologies (ESIB)
    Université Saint Joseph
    Mar Roukos-Mkallès
    P.O. Box 1514 Riad El Solh
    Beirut 1107 2050, Lebanon
    e-mail

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