Year: 2015
Type: article
Abstract: 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 consider two more versions of octahedrality, which are 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.
Source: Journal of convex analysis
DOI: 10.68381/jca22021
Authors: Rainis Haller, Johann Langemets, Märt Põldvere
Institution: University of Tartu
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1505534160