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arXiv · 1502.02760

The Daugavet property in the Musielak-Orlicz spaces

Anna Kamińska·Damian Kubiak
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Abstract

We show that among all Musielak-Orlicz function spaces on a $\sigma$-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.

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Anna Kamińska, Damian Kubiak. 2015-02-10. The Daugavet property in the Musielak-Orlicz spaces. https://doi.org/10.1016/j.jmaa.2015.02.035

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