The Daugavet property in the Musielak-Orlicz spaces


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 L1, L∞, L1 ⊕1 L∞ and L1 ⊕∞ L∞. In particular, we obtain complete characterizations of the Daugavet property in the weighted interpolation spaces, the variable exponent Lebesgue spaces (Nakano spaces) and the Orlicz spaces.

Publication Title

Journal of Mathematical Analysis and Applications