The Daugavet property in the Musielak-Orlicz spaces

Anna Kamińska; Damian Kubiak

doi:10.1016/j.jmaa.2015.02.035

paper

The Daugavet property in the Musielak-Orlicz spaces

arXiv:1502.02760 · doi:10.1016/j.jmaa.2015.02.035

Abstract

We show that among all Musielak-Orlicz function spaces on a $σ$ -finite non-atomic complete measure space equipped with either the Luxemburg norm or the Orlicz norm the only spaces with the Daugavet property are $L_{1}$ , $L_{\infty}$ , $L_{1} \oplus_{1} L_{\infty}$ and $L_{1} \oplus_{\infty} L_{\infty}$ . We obtain in particular complete characterizations of the Daugavet property in the weighted interpolation spaces, the variable exponent Lebesgue spaces (Nakano spaces) and the Orlicz spaces.

20 pages

References in corpus (1)

Remarks on diameter 2 properties