## 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

### Keywords:

extreme norms; norms on $$\mathbb{R}^2$$; extreme elements
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