Completeness on locally convex cones

Mohammad Reza Motallebi

doi:10.1016/j.crma.2014.09.005

Mathematical analysis/Functional analysis

Completeness on locally convex cones

Presented by: the Editorial Board

Mohammad Reza Motallebi ¹

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, P.O. Box 179, Iran

Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 785-789.

is referenced by Corrigendum to the note “Completeness on locally convex cones” [C. R. Acad. Sci. Paris, Ser. I 352 (10) (2014) 785–789]

Abstract
Résumé

We investigate complete and compact subsets for the lower, upper and symmetric topologies of a locally convex cone and prove that weakly closed sets will be weakly compact, whenever they are weakly precompact. This leads to the weak* compactness of the polars of neighborhoods and weak compactness of the lower, upper and symmetric neighborhoods.

Nous étudions des sous-ensembles complets et compacts pour le bas, le haut et les topologies symétriques d'un cône localement convexe, et prouvons que les ensembles faiblement fermés sont faiblement compacts à chaque fois qu'ils sont faiblement précompacts. Cela conduit à la faible* compacité des polaires des quartiers et à la faible compacité des quartiers inférieur, supérieur et symétrique.

Received: 2014-04-29
Accepted: 2014-09-05
Published online: 2014-09-26

DOI: 10.1016/j.crma.2014.09.005

Author's affiliations:

Mohammad Reza Motallebi ¹

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, P.O. Box 179, Iran

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     title = {Completeness on locally convex cones},
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     doi = {10.1016/j.crma.2014.09.005},
     language = {en},
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Mohammad Reza Motallebi. Completeness on locally convex cones. Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 785-789. doi : 10.1016/j.crma.2014.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.005/

References
Cited by

[1] K. Keimel; W. Roth Ordered Cones and Approximation, Lect. Notes Math., vol. 1517, Springer Verlag, Heidelberg, Berlin, New York, 1992

[2] M.R. Motallebi; H. Saiflu Duality on locally convex cones, J. Math. Anal. Appl., Volume 337 (2008), pp. 888-905

[3] M.R. Motallebi; D.H. Saiflu Products and direct sums in locally convex cones, Can. Math. Bull., Volume 55 (2012) no. 4, pp. 783-798

[4] W. Roth Locally convex lattice cones, J. Convex Anal., Volume 16 (2009), pp. 1-31

[5] W. Roth Operator-Valued Measures and Integrals for Cone-Valued Functions, Lect. Notes Math., vol. 1964, Springer Verlag, Heidelberg, Berlin, New York, 2009

[6] S. Willard General Topology, Addison-Wesley, Reading, 1970

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