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.
- 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
- Received: 2013-07-19.
- Revised: 2013-08-13.
- Accepted: 2013-08-13.
