Funksjonalanalyse

• Abrahamsen, Trond A.; Hájek, Petr; Lima, Vegard & Troyanski, Stanimir (2026). Strictly convex norms and the local diameter two property. Revista Matemática Complutense. ISSN 1139-1138. 39, s. 857–877. doi: 10.1007/s13163-025-00559-z. Fulltekst i vitenarkiv Vis sammendrag

  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 $$c_0(\Gamma )$$ c 0 ( 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 $$c_0({\mathbb {N}}),$$ c 0 ( 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 $$c_0(\Gamma ),$$ c 0 ( Γ ) , where $$\Gamma $$ Γ is uncountable, for which the space has a 1-unconditional basis and the local diameter two property.

• Haller, Rainis; Kaasik, Jaan Kristjan & Ostrak, Andre (2026). The local diameter two property and the diameter two property in spaces of Lipschitz functions. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 556(1). doi: 10.1016/j.jmaa.2025.130178. Fulltekst i vitenarkiv Vis sammendrag

  We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the w⁎-LD2P, the w⁎-D2P, the LD2P, and the SD2P in these spaces. We introduce a generalised version of cyclical monotonicity to study functionals on spaces of Lipschitz functions.

• Haller, Rainis; Kaasik, Jaan Kristjan & Ostrak, Andre (2025). Separating diameter two properties from their weak-star counterparts in spaces of Lipschitz functions. Studia Mathematica. ISSN 0039-3223. 280 (1), s. 87–102. doi: 10.4064/sm240612-9-9. Fulltekst i vitenarkiv Vis sammendrag

  We address some open problems concerning Banach spaces of real-valued Lipschitz functions. Specifically, we prove that the diameter 2 properties differ from their weak-star counterparts in these spaces. In particular, we establish the existence of dual Banach spaces lacking the symmetric strong diameter 2 property but possessing its weakstar counterpart. We show that there exists an octahedral Lipschitz-free space whose bidual is not octahedral. Furthermore, we prove that the Banach space of real-valued Lipschitz functions from any infinite subset of ℓ1 possesses the symmetric strong diameter 2 property. These results are achieved by introducing new sufficient conditions, providing new examples and clarifying the status of known ones.

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