A Weierstrass-Stone theorem for Choquet simplexes

 Access to full text

 Full (PDF)

1. [1] T. ANDÔ, On fundamental properties of a Banach space with a cone, Pacific Journ. Math., 12 (1962), 1163-1169. Zbl0123.30802MR27 #568
2. [2] H. BAUER, Minimalstellen von Funktionen und Extremalpunkte II, Arch. Math. 11 (1960), 200-205. Zbl0098.08003MR24 #A251
3. [3] H. BAUER, Konvexität in topologischen Vektorräumen, Xerographed lecture notes, Hamburg 1963/1964. 
4. [4] E. BISHOP and K. DE LEEUW, The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier, Grenoble, 11 (1961), 89-136. 
5. [5] N. BOURBAKI, Intégration (Chapitres 1-4), 2ième édition, Hermann, Paris 1965. Zbl0136.03404
6. [6] G. CHOQUET and P.-A. MEYER, Existence et unicité des représentations intégrales dans les convexes compacts quelconques, Ann. Inst. Fourier, Grenoble, 13 (1963), 139-154. Zbl0122.34602MR26 #6748
7. [7] D.A. EDWARDS, The homeomorphic affine embedding of a locally compact cone into a Banach dual space endowed with the vague topology, Proc. Lond. Math. Soc. 14 (1964), 399-414. Zbl0205.12202MR29 #6274
8. [8] D.A. EDWARDS, Séparation des fonctions réelles définies sur un simplexe de Choquet, C.R. Acad. Sci. Paris 261 (1965), 2798-2800. Zbl0156.13301MR32 #8131
9. [9] D.A. EDWARDS, On separation and approximation of real functions defined on a Choquet simplex, Proc. Second Prague Topological Symposium (1966), 122-128. Zbl0177.16302
10. [10] D.A. EDWARDS, The affine continuous functions on a Choquet simplex, Proc. Bruges Summer School on Topological Algebra Theory (1966), Brussels 1967. Zbl0184.34401
11. [11] E.G. EFFROS, Structure in simplexes, Acta Math. 117 (1967), 103-121. Zbl0154.14201MR34 #3287
12. [12] S. KAKUTANI, Concrete representation of abstract (M)-spaces, Ann. of Math. 42 (1941), 994-1024. Zbl0060.26604
13. [13] J. LINDENSTRAUSS, Extension of compact operators, Mem. Amer. Math. Soc. 48, Providence, R.I., (1964). Zbl0141.12001MR31 #3828
14. [14] P.-A. MEYER, Probabilités et potentiel, Hermann, Paris, (1966). Zbl0138.10402MR34 #5118
15. [15] R.R. PHELPS, Lectures on Choquet's theorem, van Nostrand, Princeton N.J., 1966. Zbl0135.36203MR33 #1690
16. [16] F. RIESZ, Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math. 41 (1940), 174-206. Zbl0022.31802MR1,147dJFM66.0553.01

1. Hicham Fakhoury, Projections de meilleure approximation continues dans certains espaces de Banach
2. Hicham Fakhoury, Espaces fortement réticulés de fonctions affines
3. G. F. Vincent-Smith, Uniform approximation of harmonic functions
4. Ian Reay, Subduals and tensor products of spaces of harmonic functions