Duality of non-locally convex Orlicz spaces.(English)Zbl 0801.46029

Summary: The topological dual of an Orlicz space $$L^ \varphi$$ defined by an arbitrary finite valued Orlicz function $$\varphi$$ (not necessarily convex) over a $$\sigma$$-finite atomless measure space is described. The well known results concerning the duality of locally convex Orlicz spaces are generalized.

MSC:

 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B10 Duality and reflexivity in normed linear and Banach spaces 46B42 Banach lattices