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Extreme points of lattice intervals in the Minkowski-Rådström-Hörmander lattice
Author(s):
Jerzy
Grzybowski;
Ryszard
Urbanski
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3957-3962.
MSC (2000):
Primary 46B20, 52A05, 54B20
Posted:
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  over any Hausdorff topological vector space  (Theorem 1). Then we prove that the unit ball in the Minkowski-Rådström-Hörmander lattice  over any normed space  , dim 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 Poznan, Poland
Email:
jgrz@amu.edu.pl
Ryszard
Urbanski
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
Email:
rich@amu.edu.pl
DOI:
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
Posted:
June 3, 2008
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2008,
Jerzy Grzybowski and Ryszard Urba\'nski
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