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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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


Authors: Jerzy Grzybowski and Ryszard Urbanski
Journal: Proc. Amer. Math. Soc. 136 (2008), 3957-3962
MSC (2000): Primary 46B20, 52A05, 54B20
Published electronically: June 3, 2008
MathSciNet review: 2425736
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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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Additional Information

Jerzy Grzybowski
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Email: jgrz@amu.edu.pl

Ryszard Urbanski
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Email: rich@amu.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09376-3
PII: S 0002-9939(08)09376-3
Keywords: Minkowski--R{\aa }dstr{\"o}m--H{\"o}rmander lattices, extreme points, pairs of closed bounded convex sets
Received by editor(s): March 13, 2007
Received by editor(s) in revised form: October 4, 2007
Published electronically: June 3, 2008
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 Jerzy Grzybowski and Ryszard Urba\'nski