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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extreme points of lattice intervals in the Minkowski-Rådström-Hörmander lattice
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by Jerzy Grzybowski and Ryszard Urbański PDF
Proc. Amer. Math. Soc. 136 (2008), 3957-3962

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 Urbański
  • Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
  • Email: rich@amu.edu.pl
  • 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
  • © Copyright 2008 Jerzy Grzybowski and Ryszard Urbański
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3957-3962
  • MSC (2000): Primary 46B20, 52A05, 54B20
  • DOI: https://doi.org/10.1090/S0002-9939-08-09376-3
  • MathSciNet review: 2425736