Rainis Haller, Senior Research Fellow, University of Tartu
Olav Nygaard, professor, Unioversity of Agder, Norway
Ginés López Pérez, professor, Granada University, Spain
Jarno Talponen, vanemteadur, University of Eastern Finland, Finland
In the geometry of Banach spaces structure of the unit ball plays an important role. Previously, various properties and notions describing Banach spaces whose unit ball has slices with arbitrarily small diameter have been extensively studied, for example, the Radon–Nikodým property, denting points or strongly exposed points. Lately, the extreme opposite property – Banach spaces with all slices of the unit ball having diameter equal to 2 – has gotten some extra attention. For example, the classical Banach spaces c0, ℓ∞, C[0,1], and L1[0,1] all have this property. These spaces even have the property that every nonempty relatively weakly open subset (in particular a slice) of their unit ball has diameter equal to 2. The latter property is called the diameter 2 property. In the current thesis, diameter 2 property and similar properties are studied, dual spaces of diameter 2 spaces are characterized in terms of octahedrality, stability results of diameter 2 properties are presented, and relations between diameter 2 structure of spaces of operators and corresponding Banach spaces are investigated.