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

Robert R. Phelps

Annales de l'institut Fourier (1970)

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

Abstract

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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 ) .

How to cite

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Phelps, 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

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  1. [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. [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. [3] N. BOURBAKI, Espaces vectoriels topologiques, Ch. 1 et 2, 2e édition, Paris, 1966. 
  4. [4] N. DINCULEANU, Vector measures, Berlin, 1967. 
  5. [5] N. DUNFORD and J. T. SCHWARTZ, Linear operators Part I, (1958), Interscience. Zbl0084.10402
  6. [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. [7] G. SEEVER, Generalization of a theorem of Lindenstrauss (dittoed notes). Zbl0289.46035

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