This is an announcement for the paper "On duality of diameter 2 properties" by Rainis Haller, Johann Langemets and Mart Poldvere.

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 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B22

Submitted from: johann.langemets@ut.ee

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1311.2177

or

http://arXiv.org/abs/1311.2177