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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
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