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

Abstract

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