Zenon Zbąszyniak (1994)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.
Henryk Hudzik, Zenon Zbąszyniak (1993)
Colloquium Mathematicae
Similarity:
Henryk Hudzik, Zenon Zbaszyniak (1997)
Collectanea Mathematica
Similarity:
A formula for the distance of an arbitrary element x in Musielak-Orlicz space L^Phi from the subspace E^Phi of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of L^Phi is given for any of these two norms. Criteria for smooth points and smoothness in L^Phi and E^Phi equipped with the Orlicz norm are presented.
Małgorzata Doman (1991)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We give necessary and sufficient conditions for weak uniform rotundity of Musielak–Orlicz spaces with the Luxemburg norm. The result is a generalization of a theorem by Kami’nska and Kurc.
Ji Donghai, Yanming Lü, Ting Fu Wang (1998)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
Nearly smooth points and near smoothness in Orlicz spaces are characterized. It is worth to notice that in the nonatomic case smooth points and nearly smooth points are the same, but in the sequence case they differ.