Rainis Haller, Johann Langemets, Märt Põldvere
Published 2013-11-09Version 1
It is known that a Banach space has the strong diameter 2 property (i.e. every convex combination of slices of the unit ball has diameter 2) if and only if the norm on its dual space is octahedral (a notion introduced by Godefroy and Maurey). We introduce two more versions of octahedrality, which turn out to be dual properties to the diameter 2 property and its local version (i.e., respectively, every relatively weakly open subset and every slice of the unit ball has diameter 2). We study stability properties of different types of octahedrality, which, by duality, provide easier proofs of many known results on diameter 2 properties.
Slices in the unit ball of a uniform algebra
The universality of $\ell_1$ as a dual space
The unit ball of the predual of $H^\infty(\mathbb{B}_d)$ has no extreme points
![QR code for arXiv:1311.2177 [math.FA]](http://oss.arxitics.com/images/favicon.svg)