2019/02/28 by Johann Langemets, Ginés López-Pérez · 6 citations
Computer Science · Mathematics · #Advanced Banach Space Theory #Banach manifold #Banach space #Characterization (materials science) #Class (philosophy) #Dual (grammatical number) #Holomorphic and Operator Theory #Norm (philosophy) #Optimization and Variational Analysis #Separable space #math.FA #msc:46B03 #msc:46B20 #msc:46B22
paper · pdf · doi:10.1017/s1474748019000264
published in Journal of the Institute of Mathematics of Jussieu 20(2), 569-585 (Cambridge University Press) · Compared to the previous version, we have now fixed a mistake that appeared in Proposition 2.5 and added a new Corollary 4.3
openalex created_date 2019/02/21 · arxiv created 2019/04/11 · openalex publication_date 2019/05/16 · arxiv updated 2021/07/01 · openalex updated_date 2026/08/05
Abstract We prove that every separable Banach space containing an isomorphic copy of ℓ 1 can be equivalently renormed so that the new bidual norm is octahedral. This answers, in the separable case, a question in Godefroy [Metric characterization of first Baire class linear forms and octahedral norms, Studia Math. 95 (1989), 1–15]. As a direct consequence, we obtain that every dual Banach space, with a separable predual and failing to be strongly regular, can be equivalently renormed with a dual norm to satisfy the strong diameter two property.