Geodesic
On Duality of Diameter 2 Properties
Journal of convex analysis, Tome 22 (2015) no. 2, pp. 465-483
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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.
Classification : 46B20, 46B22
Mots-clés : Diameter 2 property, slice, relatively weakly open set, octahedral norm 
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     author = {R. Haller and J. Langemets and M. P\~oldvere},
     title = {On {Duality} of {Diameter} 2 {Properties}},
     journal = {Journal of convex analysis},
     pages = {465--483},
     year = {2015},
     volume = {22},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_2_JCA_2015_22_2_a6/}
}
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R. Haller; J. Langemets; M. Põldvere. On Duality of Diameter 2 Properties. Journal of convex analysis, Tome 22 (2015) no. 2, pp. 465-483. http://geodesic.mathdoc.fr/item/JCA_2015_22_2_JCA_2015_22_2_a6/