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

 

Norm-closure of the barrier cone in normed linear spaces


Authors: Samir Adly, Emil Ernst and Michel Théra
Journal: Proc. Amer. Math. Soc. 132 (2004), 2911-2915
MSC (2000): Primary 46N10, 47N10
Published electronically: May 12, 2004
MathSciNet review: 2063110
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Abstract: The aim of this note is to characterize the norm-closure of the barrier cone of a closed convex set in an arbitrary normed linear space by means of a new geometric object, the temperate cone.


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Additional Information

Samir Adly
Affiliation: LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France
Email: adly@unilim.fr

Emil Ernst
Affiliation: Laboratoire de Modélisation en Mécanique et Thermodynamique (LMMT), Casse 322, Faculté de Sciences et Techniques de Saint Jérome, Avenue Escadrille Normandie-Niemen 13397 Marseille Cedex 20, France
Email: Emil.Ernst@univ.u-3mrs.fr

Michel Théra
Affiliation: LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France
Email: michel.thera@unilim.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07492-1
PII: S 0002-9939(04)07492-1
Keywords: Fenchel conjugate, barrier cone, temperate cone, linearly bounded set, recession cone
Received by editor(s): July 15, 2002
Published electronically: May 12, 2004
Additional Notes: The third author’s research was partially supported by the French Chilean Scientific Cooperation Programme ECOS under grant C00E05 and by NATO Collaborative Linkage Grant 978488.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2004 American Mathematical Society