Opuscula Math. 34, no. 1 (2014), 161-169
http://dx.doi.org/10.7494/OpMath.2014.34.1.161

Opuscula Mathematica

Asymptotically isometric copies of c0 in Musielak-Orlicz spaces

Agata Narloch
Lucjan Szymaszkiewicz

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.

Full text (pdf)

• Agata Narloch
• University of Szczecin, Institute of Mathematics, Wielkopolska 15, 70-451 Szczecin, Poland
• Lucjan Szymaszkiewicz
• University of Szczecin, Institute of Mathematics, Wielkopolska 15, 70-451 Szczecin, Poland
• Revised: 2013-08-13.
• Accepted: 2013-08-13.