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Smooth points in Orlicz sequence spaces and geometry of the dual and the bidual of Orlicz spaces. (English) Zbl 0892.46021

Summary: Smooth points of Orlicz sequence spaces equipped with the Orlicz norm are characterized. Criteria for smoothness of \(h^\Phi_0\) and \(\ell^\Phi_0\) are deduced. Next, geometry of the dual and the bidual of Orlicz space for both (the Luxemburg and the Orlicz) norms is considered.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A45 Sequence spaces (including Köthe sequence spaces)
46B25 Classical Banach spaces in the general theory
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