Asymptotically isometric copies of c0 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 \(c_0\).
Mathematics Subject Classification: 46E30.