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
[Intégralité de cônes localement convexes]

Présenté par : 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.

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

Résumé
Abstract

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.

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.

Reçu le : 2014-04-29
Accepté le : 2014-09-05
Publié le : 2014-09-26

DOI : 10.1016/j.crma.2014.09.005

Affiliations des auteurs :

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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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/

Bibliographie
Cité par

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M. R. Motallebi Boundedness components and Ekeland's type variational principles in locally convex cones, Optimization (2025), p. 1 | DOI:10.1080/02331934.2025.2478193
M. R. Motallebi A type of minimal and maximal point theorem in locally convex product cones, Optimization, Volume 74 (2025) no. 4, p. 939 | DOI:10.1080/02331934.2023.2277718
A. Azizi Mayvan; M. R. Motallebi Optimization problems for locally convex cone-valued functions, Indian Journal of Pure and Applied Mathematics, Volume 53 (2022) no. 4, p. 865 | DOI:10.1007/s13226-021-00192-8
A. Azizi Mayvan; M. R. Motallebi Ekeland’s type variational principle for locally convex cone-valued functions, Journal of Fixed Point Theory and Applications, Volume 23 (2021) no. 4 | DOI:10.1007/s11784-021-00902-z
M. R. Motallebi Weak compactness in locally convex cones, Positivity, Volume 23 (2019) no. 2, p. 303 | DOI:10.1007/s11117-018-0607-0
M. R. Motallebi Locally convex inductive limit cones, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 112 (2018) no. 4, p. 1431 | DOI:10.1007/s13398-017-0432-5
Mohammad Reza Motallebi Weak compactness of direct sums in locally convex cones, Studia Scientiarum Mathematicarum Hungarica, Volume 55 (2018) no. 4, p. 487 | DOI:10.1556/012.2018.55.4.1407
M. R. Motallebi On weak completeness of products and direct sums in locally convex cones, Periodica Mathematica Hungarica, Volume 75 (2017) no. 2, p. 322 | DOI:10.1007/s10998-017-0201-4

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