Extreme points of lattice intervals in the Minkowski-Rådström-Hörmander lattice

Grzybowski, Jerzy; Urbański, Ryszard

doi:10.1090/S0002-9939-08-09376-3

Extreme points of lattice intervals in the Minkowski-Rådström-Hörmander lattice
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by Jerzy Grzybowski and Ryszard Urbański

Proc. Amer. Math. Soc. 136 (2008), 3957-3962

DOI: https://doi.org/10.1090/S0002-9939-08-09376-3

Published electronically: June 3, 2008

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Abstract:

In this paper we characterize extreme points of any symmetric interval in the Minkowski–Rådström–Hörmander lattice $\widetilde {X}$ over any Hausdorff topological vector space $X$ (Theorem 1). Then we prove that the unit ball in the Minkowski–Rådström–Hörmander lattice $\widetilde {X}$ over any normed space $X$, dim$X\geq 2,$ has exactly two extreme points (Theorem 2).

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