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 L1L1, L∞L∞, L1⊕1L∞L1⊕1L∞ and L1⊕∞L∞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.