Geodesic
Property (α) on Locally Convex Spaces
Journal of convex analysis, Tome 25 (2018) no. 3, pp. 1013-1017
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We study property (α) for closed convex subsets of locally convex spaces and we prove that the quasi drop property implies property (α). Moreover, if the locally convex space is complete, property (α) implies weak compactness. Thus, if every closed, convex and bounded subset of a complete locally convex spaces E has property (α), then E is semi-reflexive.
Classification : 46B20, 46B50
Mots-clés : Property alpha, drop property, weak compactness, index of non-compactness 
@article{JCA_2018_25_3_JCA_2018_25_3_a14,
     author = {I. Monterde and V. Montesinos},
     title = {Property (\ensuremath{\alpha}) on {Locally} {Convex} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {1013--1017},
     year = {2018},
     volume = {25},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_3_JCA_2018_25_3_a14/}
}
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I. Monterde; V. Montesinos. Property (α) on Locally Convex Spaces. Journal of convex analysis, Tome 25 (2018) no. 3, pp. 1013-1017. http://geodesic.mathdoc.fr/item/JCA_2018_25_3_JCA_2018_25_3_a14/