Contractive and optimal sets in Musielak-Orlicz spaces with a smoothness condition

Abstract

In this paper we use our recent generalization of a theorem of Jamison- -Kami«ska-Lewicki (characterizing one-complemented subspaces in Musielak-Orlicz sequence spaces defined by Musielak-Orlicz functions satisfying a general smoothness condition) in or- der to compare contractive and optimal sets in finite-dimensional Musielak-Orlicz ' (n) spaces in the spirit of Kami«ska-Lewicki. We also give an example illustrating the importance of the smoothness assumptions in our theorem.