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Order continuous linear functionals on non-locally convex Orlicz spaces. (English) Zbl 0812.46017

Summary: The space of all order continuous linear functionals on an Orlicz space \(L^ \varphi\) defined by an arbitrary (not necessarily convex) Orlicz function \(\varphi\) is described.

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
46A80 Modular spaces
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