Let E be a (IV)-polyhedral Banach space. We show that, for each epsilon > 0, E admits an epsilon-equivalent (V)-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its extreme points. In particular, every separable isomorphically polyhedral Banach space has this property.
De Bernardi, C. A., Unit balls of polyhedral Banach spaces with many extreme points, <<STUDIA MATHEMATICA>>, 2024; 275 (2): 175-196. [doi:10.4064/sm230710-31-12] [https://hdl.handle.net/10807/283377]
Unit balls of polyhedral Banach spaces with many extreme points
De Bernardi, Carlo Alberto
2024
Abstract
Let E be a (IV)-polyhedral Banach space. We show that, for each epsilon > 0, E admits an epsilon-equivalent (V)-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its extreme points. In particular, every separable isomorphically polyhedral Banach space has this property.
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