Geodesic
An Analog of the Krein--Mil'man Theorem for Strongly Convex Hulls in Hilbert Space
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 37-42

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the following theorem: in Hilbert space a closed bounded set is contained in the strongly convex $R$-hull of its $R$-strong extreme points. $R$-strong extreme points are a subset of the set of extreme points (it may happen that these two sets do not coincide); the strongly convex $R$-hull of a set contains the closure of the convex hull of the set. 
@article{MZM_2002_71_1_a3,
     author = {M. V. Balashov},
     title = {An {Analog} of the {Krein--Mil'man} {Theorem} for {Strongly} {Convex} {Hulls} in {Hilbert} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {37--42},
     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a3/}
}
TY  - JOUR
AU  - M. V. Balashov
TI  - An Analog of the Krein--Mil'man Theorem for Strongly Convex Hulls in Hilbert Space
JO  - Matematičeskie zametki
PY  - 2002
SP  - 37
EP  - 42
VL  - 71
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a3/
LA  - ru
ID  - MZM_2002_71_1_a3
ER  - 
%0 Journal Article
%A M. V. Balashov
%T An Analog of the Krein--Mil'man Theorem for Strongly Convex Hulls in Hilbert Space
%J Matematičeskie zametki
%D 2002
%P 37-42
%V 71
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a3/
%G ru
%F MZM_2002_71_1_a3
M. V. Balashov. An Analog of the Krein--Mil'man Theorem for Strongly Convex Hulls in Hilbert Space. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 37-42. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a3/