Geodesic
Convex-compact sets and Banach discs
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 773-780 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual $E'$ of a locally convex space $E$ is the $\sigma (E',E)$-closure of the union of countably many $\sigma (E',E)$-relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual $E'$ of a locally convex space $E$ is the $\sigma (E',E)$-closure of the union of countably many $\sigma (E',E)$-relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
Classification : 46A03, 46A50
Keywords: weakly compact sets; convex-compact sets; Banach discs 
@article{CMJ_2009_59_3_a15,
     author = {Monterde, I. and Montesinos, V.},
     title = {Convex-compact sets and {Banach} discs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {773--780},
     year = {2009},
     volume = {59},
     number = {3},
     mrnumber = {2545655},
     zbl = {1224.13023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a15/}
}
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Monterde, I.; Montesinos, V. Convex-compact sets and Banach discs. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 773-780. http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a15/