Diameter two properties and polyhedrality
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We study the (possible) relation between diameter two properties and various notions of polyhedrality. I-polyhedral spaces (being non-reflexive, M-embedded) have the strong diameter two property; however it turns out that even in II-polyhedral spaces the unit ball may contain slices of small diameter.
KeywordsPolyhedral Banach spaces Diameter two property Slices
Mathematics Subject Classification46B20
The authors want to thank an anonymous referee for suggestions that improved the exposition.