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Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm. (English) Zbl 0823.46033
Summary: A criterion for an arbitrary element from the unit sphere of a Musielak- Orlicz function space equipped with the Luxemburg norm to be a point of smoothness is given. Next, as a corollary, a criterion of smoothness of these spaces is given.

MSC:
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B20 Geometry and structure of normed linear spaces
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