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

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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 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.

MSC(Primary)46B20
MSC(Secondary)46B25
Uncontrolled Keywordsabsolute normalized norm, extreme point