Reflexive subspaces of some Orlicz spaces

Emmanuelle Lavergne

doi:10.4064/cm113-2-13

Geodesic

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Reflexive subspaces of some Orlicz spaces

Emmanuelle Lavergne ¹

¹ Laboratoire 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

Colloquium Mathematicum, Tome 113 (2008) no. 2, pp. 333-340.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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.

DOI : 10.4064/cm113-2-13

Keywords: conjugate orlicz function phi satisfies growth condition delta reflexive subspaces phi closed norm purpose proof result alexopoulos saying weakly compact subsets phi have equi absolutely continuous norm

Affiliations des auteurs :

Emmanuelle Lavergne ¹

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Emmanuelle Lavergne. Reflexive subspaces of some Orlicz spaces. Colloquium Mathematicum, Tome 113 (2008) no. 2, pp. 333-340. doi : 10.4064/cm113-2-13. http://geodesic.mathdoc.fr/articles/10.4064/cm113-2-13/

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