Theorems of Krein Milman type for certain convex sets of functions operators
Annales de l'Institut Fourier, Volume 20 (1970) no. 2, p. 45-54

Sufficient conditions are given in order that, for a bounded closed convex subset $B$ of a locally convex space $E$, the set $C\left(X,B\right)$ of continuous functions from the compact space $X$ into $B$, is the uniformly closed convex hull in $C\left(X,E\right)$ of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into $C\left(X\right)$.

On donne des conditions suffisantes sous lesquelles, pour un convexe borné fermé $B$ d’un espace localement convexe réel $E$, l’ensemble $C\left(X,B\right)$ [des fonctions continues de l’espace compact $X$ dans $B$] est l’enveloppe convexe uniformément fermée dans $C\left(X,E\right)$ de ses points extrémaux. On applique ces résultats à la boule unité de l’espace d’opérateurs bornés (ou compacts, ou faiblement compacts) de certains espaces de Banach dans $C\left(X\right)$.

@article{AIF_1970__20_2_45_0,
author = {Phelps, Robert R.},
title = {Theorems of Krein Milman type for certain convex sets of functions operators},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Durand},
address = {28 - Luisant},
volume = {20},
number = {2},
year = {1970},
pages = {45-54},
doi = {10.5802/aif.351},
zbl = {0195.40807},
mrnumber = {44 \#4501},
language = {en},
url = {http://www.numdam.org/item/AIF_1970__20_2_45_0}
}

Phelps, Robert R. Theorems of Krein Milman type for certain convex sets of functions operators. Annales de l'Institut Fourier, Volume 20 (1970) no. 2, pp. 45-54. doi : 10.5802/aif.351. http://www.numdam.org/item/AIF_1970__20_2_45_0/

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