Bidual octahedral renormings and strong regularity in Banach spaces

• Published in: arXiv.org
• Main Authors: Langemets, Johann, López-Pérez, Ginés
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.04.2019
• Subjects: Banach spaces; Equivalence; Mathematics - Functional Analysis

We prove that every separable Banach space containing \(\ell_1\) can be equivalently renormed so that its bidual space is octahedral, which answers, in the separable case, a question by Godefroy in 1989. As a direct consequence, we obtain that every dual Banach space, with a separable predual, faili...