Asymptotically isometric copies of c_{0} 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 \(c_0\) in the subspaces of order continuous elements in Orlicz spaces, Journal of Convex Analysis 21 (2014)] to Musielak-Orlicz spaces.

Keywords

• Musielak-Orlicz space
• Luxemburg norm
• condition \(\Delta_2\)
• asymptotically isometric copy of \(c_0\)