2024/10/24 by Trond A. Abrahamsen, Abrahamsen, Trond A., Petr Hájek +5
Computer Science · Mathematics · #46B03 #46B20 #Advanced Banach Space Theory #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2410.18473
openalex publication_date 2024/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study a strict monotonicity property of the norm in solid Banach lattices of real functions that prevents such spaces from having the local diameter two property. Then we show that any strictly convex 1-symmetric norm on c0(Γ) possesses this property. In the opposite direction, we show that any Banach space which is strictly convex renormable and contains a complemented copy of c0(\mathbb N), admits an equivalent strictly convex norm for which the space has the local diameter two property. In particular, this enables us to construct a strictly convex norm on c0(Γ), where Γ is uncountable, for which the space has a 1-unconditional basis and the local diameter two property.