Hokkaido Mathematical Journal

SAITO Kichi-Suke, MITANI Ken-Ichi, KOMURO Naoto,

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

Hokkaido Mathematical Journal, 42 (2013) pp.1-9




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 φ on [0,1] with max{1-t,t} ≤ φ(t) ≤ 1 for t ∈ [0,1] (denoted by Ψ2) are in a one to one correspondence under the equation φ(t) = ||(1-t,t)||. Recently, we characterized extreme points of AN2 by considering Ψ2. In this paper we give another proof of this result.

Uncontrolled Keywordsabsolute normalized norm, extreme point