Asymptotically isometric copies of cₒ in Musielak-Orlicz spaces

Abstract

Criteria in order that a Musielak-Orlicz function space $L^\Phi$ as well as Musielak-Orlicz sequence space $l^\Phi$ contains an asymptotically isometric copy of $c_0$ are given. These results extend some results of [Y.A. Cui, H. Hudzik, G. Lewicki, Order asymptotically isometric copies of c0 in the subspaces of order continuous elements in Orlicz spaces, Journal of Convex Analysis 21 (2014)] to Musielak-Orlicz spaces.