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Extreme norms on \(\mathbb{R}^2\). (English) Zbl 0942.46004

Suppose \(N_1\), \(N_2\) are norms on \(\mathbb{R}^2\) such that \(N_1> N_2\). Denote the set of all norms \(N\) satisfying the condition \(N_1\geq N\geq N_2\) by \({\mathcal N}(N_1, N_2)\). The purpose of this paper is to characterize the extreme elements of \({\mathcal N}(N_1, N_2)\).

MSC:

46B07 Local theory of Banach spaces
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