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.
@article{urn:eudml:doc:40795, title = {Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm.}, journal = {Collectanea Mathematica}, volume = {48}, year = {1997}, pages = {543-561}, zbl = {0904.46018}, mrnumber = {MR1602592}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40795} }
Hudzik, Henryk; Zbaszyniak, Zenon. Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm.. Collectanea Mathematica, Tome 48 (1997) pp. 543-561. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40795/