A note on extreme norms on $\mathbb R$2

Abstract

We denote by AN₂ the set of all absolute normalized norms on $\mathbb R$². It is known that the set AN₂ and the set of all continuous convex functions ψ on [0,1] with max{1−t,t} ≤ ψ(t) ≤ 1 for t ∈ [0,1] (denoted by Ψ₂) are in a one to one correspondence under the equation ψ(t) = ||(1−t,t)||. Recently, we characterized extreme points of AN₂ by considering Ψ₂. In this paper we give another proof of this result.