Reflexive subspaces of some Orlicz spaces

Volume 113 / 2008

Emmanuelle Lavergne Colloquium Mathematicum 113 (2008), 333-340 MSC: 46E30, 46B20. DOI: 10.4064/cm113-2-13

Abstract

We show that when the conjugate of an Orlicz function $\phi $ satisfies the growth condition $\Delta ^0$, then the reflexive subspaces of $L^\phi $ are closed in the $L^1$-norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such $L^\phi $ have equi-absolutely continuous norm.

Authors

  • Emmanuelle LavergneLaboratoire de Mathématiques Lens (LML)
    Équipe d'Accueil EA 2462
    Fédération CNRS Nord-Pas-de-Calais FR 2956
    Faculté des Sciences Jean Perrin
    Université d'Artois
    rue Jean Souvraz S.P. 18
    62307 Lens Cedex, France
    e-mail

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