# Theorems of Krein Milman type for certain convex sets of functions operators

Annales de l'institut Fourier (1970)

- Volume: 20, Issue: 2, page 45-54
- ISSN: 0373-0956

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topPhelps, Robert R.. "Theorems of Krein Milman type for certain convex sets of functions operators." Annales de l'institut Fourier 20.2 (1970): 45-54. <http://eudml.org/doc/74021>.

@article{Phelps1970,

abstract = {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 $C(X)$.},

author = {Phelps, Robert R.},

journal = {Annales de l'institut Fourier},

keywords = {functional analysis},

language = {eng},

number = {2},

pages = {45-54},

publisher = {Association des Annales de l'Institut Fourier},

title = {Theorems of Krein Milman type for certain convex sets of functions operators},

url = {http://eudml.org/doc/74021},

volume = {20},

year = {1970},

}

TY - JOUR

AU - Phelps, Robert R.

TI - Theorems of Krein Milman type for certain convex sets of functions operators

JO - Annales de l'institut Fourier

PY - 1970

PB - Association des Annales de l'Institut Fourier

VL - 20

IS - 2

SP - 45

EP - 54

AB - 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 $C(X)$.

LA - eng

KW - functional analysis

UR - http://eudml.org/doc/74021

ER -

## References

top- [1] ERRET BISHOP and R. R. PHELPS, The support functionals of a convex set, Proc. Symp. Pure Math. vol 7 (Convexity), A.M.S. (1963), p. 27-35. Zbl0149.08601MR27 #4051
- [2] R. M. BLUMENTHAL, J. LINDENSTRAUSS and R. R. PHELPS, Extreme operators into C(K), Pacific J. Math. 15 (1965), p. 747-756. Zbl0141.32101MR35 #758
- [3] N. BOURBAKI, Espaces vectoriels topologiques, Ch. 1 et 2, 2e édition, Paris, 1966.
- [4] N. DINCULEANU, Vector measures, Berlin, 1967.
- [5] N. DUNFORD and J. T. SCHWARTZ, Linear operators Part I, (1958), Interscience. Zbl0084.10402
- [6] P. D. MORRIS and R. R. PHELPS, Theorems of Krein-Milman type for certain convex sets of operators, Trans. Amer. Math. Soc. 150 (1970), 183-200. Zbl0198.46601MR41 #7409
- [7] G. SEEVER, Generalization of a theorem of Lindenstrauss (dittoed notes). Zbl0289.46035

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