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(X,B) of continuous functions from the compact space X into B, is the uniformly closed convex hull in C(X,E) 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(X).

On donne des conditions suffisantes sous lesquelles, pour un convexe borné fermé B d’un espace localement convexe réel E, l’ensemble C(X,B) [des fonctions continues de l’espace compact X dans B] est l’enveloppe convexe uniformément fermée dans C(X,E) 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(X).

@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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