2024/04/17 by R. Haller, Haller, Rainis, Jaan Kristjan Kaasik +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Primary 46B04 #Secondary 46B20 #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2404.11430
openalex publication_date 2024/04/17 · openalex created_date 2024/04/19 · openalex updated_date 2026/07/28
We address some open problems concerning Banach spaces of real-valued Lipschitz functions. Specifically, we prove that the diameter two 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 two property but possessing its weak-star 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 two property. These results are achieved by introducing new sufficient conditions, providing new examples and clarifying the status of known ones.