On Non-reflexive Subspaces of Orlicz Spaces

Abstract

Several geometric properties of Orlicz spaces are given. Among other things we prove that an N − function Φ satisfies the Δ ₂ condition if and only if every non-reflexive subspace of L ^Φ (μ) contains a complemented copy of ₁, if and only if L ^Φ (μ) enjoys the weak Radon-Nikodym property. We also prove that Φ ∈Δ₂ if and only if every Asplund subspace of L ^Φ (μ) is reflexive.