Year: 2026
Type: preprint
Abstract: We construct equivalent norms on $L_1[0,1]$, arbitrarily close to the usual $L_1$-norm, which are weakly midpoint locally uniformly rotund and Gâteaux smooth, and whose dual norms have the Daugavet property. In particular, we obtain a strictly convex and smooth Banach space with the Daugavet property, thereby solving a longstanding open problem in the area.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2262748287, G2550080368, G300979063, G3480869486, G410571670, G425668148, G4864075348, G5080475149, G5967599077, Extreme phenomena in Banach space geometry: small and big slices and their applications to Lipschitz-free spaces and their duals, G699191746, Plasticity and extremal geometric structure of the unit ball of Banach spaces with applications to the study of Lipschitz spaces, vector-valued functions spaces and tensor products, G7434936867, G7454915943, G7626972671, G843564687, G8738026635
OpenAlex ID: W7213117229