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February 2013 A note on extreme norms on $\mathbb R$2
Kichi-Suke SAITO, Ken-Ichi MITANI, Naoto KOMURO
Hokkaido Math. J. 42(1): 1-9 (February 2013). DOI: 10.14492/hokmj/1362406636

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.

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Kichi-Suke SAITO. Ken-Ichi MITANI. Naoto KOMURO. "A note on extreme norms on $\mathbb R$2." Hokkaido Math. J. 42 (1) 1 - 9, February 2013. https://doi.org/10.14492/hokmj/1362406636

Information

Published: February 2013
First available in Project Euclid: 4 March 2013

zbMATH: 1272.46006
MathSciNet: MR3076296
Digital Object Identifier: 10.14492/hokmj/1362406636

Subjects:
Primary: 46B20, 46B25

Rights: Copyright © 2013 Hokkaido University, Department of Mathematics

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Vol.42 • No. 1 • February 2013
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