Reflexive subspaces of some Orlicz spaces
Volume 113 / 2008
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.
