Geodesic
Reflexive subspaces of some Orlicz spaces
Emmanuelle Lavergne1
1Laboratoire 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

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

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