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

Mielczarek, Grzegorz

Acta Univ. Carol., Math. Phys. 40, No. 1, 5-20 (1999).

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 \({\mathcal N}(N_1, N_2)\).

Reviewer: J.Howard (Las Vegas/New Mexico)

MSC:

46B07

Local theory of Banach spaces

Keywords:

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