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On some convexity properties of Orlicz sequence spaces equipped with the Luxemburg norm. (English) Zbl 0899.46012
Summary: Rotundity of finite-dimensional Orlicz spaces $\ell^\Phi_n$ equipped with the Luxemburg norm is considered. It is proved that criteria for rotundity of $\ell^\Phi_n$ for $n\ge 3$ does not depend on $n$ and are the same as the criteria for rotundity of the infinite-dimensional subspace $h^\Phi$ of an Orlicz sequence space $\ell^\Phi$. Criteria for rotundity of $\ell^\Phi_2$ are different. Next, criteria for exposed points, $(H)$-points, strongly exposed points and LUR-points of the unit sphere of $\ell^\Phi$ and of its subspace $h^\Phi$ are given.

MSC:
46B25Classical Banach spaces in the general theory of normed spaces
46A45Sequence spaces
46B07Local theory of Banach spaces
46B20Geometry and structure of normed linear spaces
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