On extreme points of the dual ball of a polyhedral space

Abstract

We prove that every separable polyhedral Banach space X is isomorphic to a polyhedral Banach space Y such that, the set ext Bᵧ ∗cannot be covered by a sequence of balls B (𝓎i; 𝜖i) with 0 < 𝜖i < 1 and 𝜖i ⟶ 0. In particular ext Bᵧ ∗ cannot be covered by a sequence of norm compact sets. This generalizes a result from [7] where an equivalent polyhedral norm ⦀ ⦀ on c0 was constructed such that extB(c0;⦀· ⦀)∗ is uncountable but can be covered by a sequence of norm compact sets.